Call Now to Set Up Tutoring:

(888) 888-0446

HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

Create An Account

All HSPT Math Resources

6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Cubes

A room has dimensions of 18ft by 15ft by 9ft. The last dimension is the height of the room. It has one door that is 3ft by 7ft and two windows, each 2ft by 5ft. There is no trim to the floor, wall, doors, or windows. What is the total exposed wall space?

Possible Answers:

594 ft²

1134ft²

1093ft²

553 ft²

2389ft²

Correct answer:

553 ft²

Explanation:

If broken down into parts, this is an easy problem. It is first necessary to isolate the dimensions of the walls. If the room is 9 ft high, we know 18 x 15 designates the area of the floor and ceiling. Based on this, we know that the room has the following dimensions for the walls: 18 x 9 and 15 x 9. Since there are two of each, we can calculate the total area of walls - ignoring doors and windows - by doubling the sum of these two areas:

2 * (18 * 9 + 15 * 9) = 2 * (162 + 135) = 2 * 297 = 594 ft²

Now, we merely need to calculate the area "taken out" of the walls:

For the door: 3 * 7 = 21 ft²

For the windows: 2 * (2 * 5) = 20 ft²

The total wall space is therefore: 594 – 21 – 20 = 553 ft²

Report an Error

Example Question #2 : How To Find The Surface Area Of A Cube

A room has dimensions of 23ft by 17ft by 10ft. The last dimension is the height of the room. It has one door that is 2.5ft by 8ft and one window, 3ft by 6ft. There is no trim to the floor, wall, doors, or windows. If one can of paint covers 57 ft² of surface area. How many cans of paint must be bought to paint the walls of the room.

Possible Answers:

Correct answer:

Explanation:

If broken down into parts, this is an easy problem. It is first necessary to isolate the dimensions of the walls. If the room is 10ft high, we know 23 x 17 designates the area of the floor and ceiling. Based on this, we know that the room has the following dimensions for the walls: 23 x 10 and 17 x 10. Since there are two of each, we can calculate the total area of walls - ignoring doors and windows - by doubling the sum of these two areas:

2 * (23 * 10 + 17 * 10) = 2 * (230 + 170) = 2 * 400 = 800 ft²

Now, we merely need to calculate the area "taken out" of the walls:

For the door: 2.5 * 8 = 20 ft²

For the windows: 3 * 6 = 18 ft²

The total wall space is therefore: 800 – 20 – 18 = 762 ft²

Now, if one can of paint covers 57 ft², we calculate the number of cans necessary by dividing the total exposed area by 57: 762/57 = (approx.) 13.37.

Since we cannot buy partial cans, we must purchase 14 cans.

Report an Error

Example Question #1 : How To Find The Surface Area Of A Cube

A certain cube has a side length of 25 m. How many square tiles, each with an area of 5 m², are needed to fully cover the surface of the cube?

Possible Answers:

750

500

100

1000

200

Correct answer:

750

Explanation:

A cube with a side length of 25m has a surface area of:

25m * 25m * 6 = 3,750 m²

(The surface area of a cube is equal to the area of one face of the cube multiplied by 6 sides. In other words, if the side of a cube is s, then the surface area of the cube is 6s^2.)

Each square tile has an area of 5 m².

Therefore, the total number of square tiles needed to fully cover the surface of the cube is:

3,750m²/5m²= 750

Note: the volume of a cube with side length s is equal to s³. Therefore, if asked how many mini-cubes with side length n are needed to fill the original cube, the answer would be:

s³/n³

Report an Error

Example Question #11 : Solid Geometry

A company wants to build a cubical room around a cone so that the cone's height and diameter are 3 inch less than the dimensions of the cube. If the volume of the cone is 486π ft³, what is the surface area of the cube?

Possible Answers:

486 in²

69,984 in²

513.375 in²

726 in²

73,926 in²

Correct answer:

73,926 in²

Explanation:

To begin, we need to solve for the dimensions of the cone.

The basic form for the volume of a cone is: V = (1/3)πr²h

Using our data, we know that h = 2r because the height of the cone matches its diameter (based on the prompt).

486π = (1/3)πr²* 2r = (2/3)πr³

Multiply both sides by (3/2π): 729 = r³

Take the cube root of both sides: r = 9

Note that this is in feet. The answers are in square inches. Therefore, convert your units to inches: 9 * 12 = 108, then add 3 inches to this: 108 + 3 = 111 inches.

The surface area of the cube is defined by: A = 6 * s², or for our data, A = 6 * 111² = 73,926 in²

Report an Error

Example Question #2 : Non Cubic Prisms

Angie is painting a 2 foot cube for a play she is in. She needs $25\hspace{1 mm}mL$ of paint for every square foot she paints. How much paint does she need?

Possible Answers:

$600\hspace{1 mm}mL$

$1.041\overline{6}\hspace{1 mm}mL$

$100\hspace{1 mm}mL$

None of the available answers

It is impossible to convert between metric units and feet.

Correct answer:

$600\hspace{1 mm}mL$

Explanation:

First we must calculate the surface area of the cube. We know that there are six surfaces and each surface has the same area:

$Area=6(2^2)=6\times 4=24\hspace{1 mm}feet^2$

Now we will determine the amount of paint needed

$24\hspace{1 mm}feet^2\times \frac{25\hspace{1 mm}mL}{1\hspace{1 mm}foot^2}=600\hspace{1 mm}mL$

Report an Error

Example Question #1 : How To Find The Surface Area Of A Sphere

A spherical orange fits snugly inside a small cubical box such that each of the six walls of the box just barely touches the surface of the orange. If the volume of the box is 64 cubic inches, what is the surface area of the orange in square inches?

Possible Answers:

64π

256π

128π

16π

32π

Correct answer:

16π

Explanation:

The volume of a cube is found by V = s³. Since V = 64, s = 4. The side of the cube is the same as the diameter of the sphere. Since d = 4, r = 2. The surface area of a sphere is found by SA = 4π(r²) = 4π(2²) = 16π.

Report an Error

Example Question #241 : Geometry

Steve's bedroom measures 20' by 18' by 8' high. He wants to paint the ceiling and all four walls using a paint that gets 360 square feet of coverage per gallon. A one-gallon can of the paint Steve wants costs $36.00; a one-quart can costs $13.00. What is the least amount of money that Steve can expect to spend on paint in order to paint his room?

Possible Answers:

$\$98$

$\$111$

$\$108$

$\$121$

$\$85$

Correct answer:

$\$108$

Explanation:

Two of the walls have area $20 \cdot 8 = 160\;\textrm{in}^{2}$ ; two have area $18 \cdot 8 = 144\;\textrm{in}^{2}$ ; the ceiling has area $20 \cdot 18 = 360\;\textrm{in}^{2}$ .

Therefore, the total area Steve wants to cover is

$A = 160 + 160 + 144 + 144 + 360 =968 \; \textrm{in}^{2}$

Divide 968 by 360 to get the number of gallons Steve needs to paint his bedroom:

$968 \div 360 \approx 2.7$

Since $2 \frac{1}{2} < 2.7 < 2\frac{3}{4}$ , Steve needs to purchase either two gallon cans and three quart cans, or three gallon cans.

The first option will cost him $36 \cdot2 + 13 \cdot3 = \$111$ ; the second option will cost him $36 \cdot3 = \$108$ . The latter is the more economical option.

Report an Error

Example Question #313 : Ssat Middle Level Quantitative (Math)

Prism

Give the surface area of the above box in square centimeters.

Possible Answers:

$216,000 \textrm { cm}^{2}$

$28,800 \textrm { cm}^{2}$

$21,600 \textrm { cm}^{2}$

$32,400 \textrm { cm}^{2}$

$324,000 \textrm { cm}^{2}$

Correct answer:

$28,800 \textrm { cm}^{2}$

Explanation:

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

$0.9 \times 100 = 90$ centimeters

$0.6 \times 100 = 60$ centimeters

Use the surface area formula, substituting L = 90, W = H = 60 :

A = 2LH + 2LW + 2HW

$A = 2 \cdot 90 \cdot 60 + 2\cdot 90 \cdot 60 + 2 \cdot 60 \cdot 60$

A = 10,800 + 10,800 + 7,200 = 28,800 square centimeters

Report an Error

Example Question #601 : Problem Solving

Square

Note: Figure NOT drawn to scale.

Refer to the above diagram, which shows a square. Give the ratio of the area of the yellow region to that of the white region.

Possible Answers:

27:5

55:9

57:7

The correct answer is not given among the other choices.

7:1

Correct answer:

55:9

Explanation:

The area of the entire square is the square of the length of a side, or

$80 \times 80 = 6,400$ .

The area of the right triangle is half the product of its legs, or

$\frac{1}{2} \times 30 \times 60 = 900$ .

The area of the yellow region is therefore the difference of the two, or

6,400 - 900 = 5,500 .

The ratio of the area of the yellow region to that of the white region is

$\frac{5,500}{900} = \frac{5,500 \div 100}{900\div 100} = \frac{55}{9}$ ; that is, 55 to 9.

Report an Error

Example Question #81 : Quadrilaterals

Swimming_pool

The above depicts a rectangular swimming pool for an apartment. The pool is five feet deep everywhere.

An apartment manager wants to paint the four sides and the bottom of the swimming pool. One one-gallon can of the paint he wants to use covers 350 square feet. How many cans of the paint will the manager need to buy?

Possible Answers:

Correct answer:

Explanation:

The bottom of the swimming pool has area

$50 \times 35 = 1,750$ square feet.

There are two sides whose area is

$50 \times 5 = 250$ square feet,

and two sides whose area is

$35 \times 5 = 175$ square feet.

Add the areas:

1,750 + 250+ 250+ 175+175= 2,600 square feet.

One one-gallon can of paint covers 350 square feet, so divide:

$2,600 \div 350 \approx 7.4$

Seven full gallons and part of another are required, so eight is the correct answer.

Report an Error

View Tutors

Samarth
Certified Tutor

Maharaja Sayajirao University of Baroda, Bachelor of Engineering, Mechanical Engineering. Concordia University-Seward, Master...

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

View Tutors

Ana Maria
Certified Tutor

Florida International University, Bachelor of Science, Mathematics Teacher Education.

All HSPT Math Resources

6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Math Tutors in San Francisco-Bay Area, Reading Tutors in Atlanta, Chemistry Tutors in Denver, LSAT Tutors in New York City, MCAT Tutors in Philadelphia, LSAT Tutors in Boston, Physics Tutors in Los Angeles, GRE Tutors in San Francisco-Bay Area, Chemistry Tutors in Atlanta, Reading Tutors in Boston

Popular Courses & Classes

GMAT Courses & Classes in Atlanta, Spanish Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Atlanta, ACT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in New York City, SSAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Washington DC, GRE Courses & Classes in Atlanta, ACT Courses & Classes in Los Angeles, SAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

GRE Test Prep in San Francisco-Bay Area, ISEE Test Prep in San Diego, LSAT Test Prep in Boston, MCAT Test Prep in New York City, SSAT Test Prep in Boston, MCAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Atlanta, LSAT Test Prep in Denver, LSAT Test Prep in Houston, ACT Test Prep in San Francisco-Bay Area

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1 : Cubes

Example Question #2 : How To Find The Surface Area Of A Cube

Example Question #1 : How To Find The Surface Area Of A Cube

Example Question #11 : Solid Geometry

Example Question #2 : Non Cubic Prisms

Example Question #1 : How To Find The Surface Area Of A Sphere

Example Question #241 : Geometry

Example Question #313 : Ssat Middle Level Quantitative (Math)

Example Question #601 : Problem Solving

Example Question #81 : Quadrilaterals

All HSPT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: