We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : Spheres

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #191 : Psat Mathematics

If a sphere has an approximate volume of $904.32\textup{ cubic meters}$ , then what is the approximate diameter of this sphere?

Possible Answers:

$17\textup{m}$

$9\textup{m}$

$12\textup{m}$

$10\textup{m}$

$15\textup{m}$

Correct answer:

$12\textup{m}$

Explanation:

The formula for the volume of a sphere is

$v=\left ( \frac{4}{3} \right )\pi r^3$

Therefore,

$904.32=\left ( \frac{4}{3} \right )\pi r^3$

Dividing both sides by $\left ( \frac{4}{3} \right )\pi$ , leaves us with $r^3\approx215.89$ . Taking the cube root, we find $r\approx5.999$ , meaning our diameter $d\approx12$ .

Report an Error

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

A cube with volume 27 cubic inches is inscribed inside a sphere such that each vertex of the cube touches the sphere. What is the radius, in inches, of the sphere?

Possible Answers:

√3/2 (approximately 1.73)

(3√3)/2 (approximately 2.60)

8.5

Correct answer:

(3√3)/2 (approximately 2.60)

Explanation:

We know that the cube has a volume of 27 cubic inches, so each side of the cube must be ∛27=3 inches. Since the cube is inscribed inside the sphere, the diameter of the sphere is the diagonal length of the cube, so the radius of the sphere is half of the diagonal length of the cube. To find the diagonal length of the cube, we use the distance formula d=√(3²+3²+3² )=√(3*3² )=3√3, and then divide the result by 2 to find the radius of the sphere, (3√3)/2.

Report an Error

Example Question #21 : Spheres

The surface area of a sphere is 100π square feet. What is the radius in feet?

Possible Answers:

100

Correct answer:

Explanation:

S = 4π(r²)

100π = 4π(r²)

100 = 4r²

25 = r²

5 = r

Report an Error

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

A spherical water tank has a surface area of 400 square meters. To the nearest tenth of a meter, give the radius of the tank.

Possible Answers:

$11.3\textup{ m}$

$5.6\textup{ m}$

$9.1\textup{ m}$

$4.6\textup{ m}$

$3.2\textup{ m}$

Correct answer:

$5.6\textup{ m}$

Explanation:

Given radius , the surface area of a sphere is given by the formula

$S = 4 \pi r^{2}$

Set S = 400 and solve for :

$4 \pi r^{2} = 400$

$4 \pi r^{2}\div 4 = 400 \div 4$

$\pi r^{2} = 100$

$\pi r^{2} \div \pi = 100 \div \pi$

$r^{2} \approx 100 \div 3.14159 \approx 31.831$

$r \approx \sqrt{31.831} \approx 5.6$ meters.

Report an Error

Example Question #4 : How To Find The Radius Of A Sphere

A spherical tank is to hold 50,000 liters of water. Given that one cubic meter is equal to 1,000 liters, give the radius of this tank to the nearest tenth of a meter.

Possible Answers:

$2.3\textup{ m}$

$3.5\textup{ m}$

$4.0 \textup{ m}$

$4.6\textup{ m}$

$2.0 \textup{ m}$

Correct answer:

$2.3\textup{ m}$

Explanation:

Given radius , the volume of a sphere is given by the formula

$V = \frac{4}{3} \pi r^{3}$

Since 1,000 liters = 1 cubic meter, 50,000 liters = 50 cubic meters, and we find by setting V= 50 :

$\frac{4}{3} \pi r^{3} = 50$

$\frac{3}{4} \cdot \frac{4}{3} \pi r^{3} = \frac{3}{4} \cdot 50$

$\pi r^{3} = 37.5$

$r^{3} =\frac{ 37.5}{\pi} \approx 11.9366$

$r \approx\sqrt[3]{ 11.9366} \approx 2.3$ meters.

Report an Error

Example Question #4 : How To Find The Radius Of A Sphere

The Kelvin temperature scale is basically the same as the Celsius scale except with a different zero point; to convert degrees Celsius to Kelvins, add 273. Also, by Charles's law, the volume of a given mass of gas varies directly as its temperature, expressed in Kelvins.

In the early morning, when the temperature is $5^{\circ }C$ , a spherical balloon is filled with helium until its radius is 100 meters. At 2:00 PM, the temperature is $20^{\circ }C$ . To the nearest tenth of a meter, what is the radius of the balloon at this time?

Possible Answers:

$98.3 \textup{ m}$

$107.2\textup{ m}$

$101.8 \textup{ m}$

$63.0\textup{ m}$

$158.7 \textup{ m}$

Correct answer:

$101.8 \textup{ m}$

Explanation:

The volume of the balloon is given by the formula

$V = \frac{4}{3} \pi r^{3}$ .

Also, by the variation relationship,

$\frac{V'}{T'} = \frac{V}{T}$

We do not need to calculate the original volume of the balloon; we can simply replace the volume with the formula:

$\frac{ \frac{4}{3} \pi r'^{3}}{T'} = \frac{ \frac{4}{3} \pi r^{3}}{T}$

Dividing both sides by $\frac{4}{3} \pi$ yields a new equation:

$\frac{ r'^{3}}{T'} = \frac{ r^{3}}{T}$

The initial radius is r = 100

The initial temperature is $T = 273 + 5 = 278 \textup{ K}$

The final (noon) temperature is $T ' = 273 + 20= 293 \textup{ K}$

Substitute to find the final radius:

$\frac{ r'^{3}}{293} = \frac{ 100^{3}}{278}$

$r'^{3} = \frac{ 1,000,000}{278} \cdot 293 \approx 1,053,957$

$r' = \approx\sqrt[3]{ 1,053,957} \approx 101.8$ meters.

Report an Error

Example Question #6 : How To Find The Radius Of A Sphere

The city of Washington wants to build a spherical water tank for the town hall. The tank is to have capacity 120 cubic meters of water.

To the nearest tenth, what will the radius of the tank be?

Possible Answers:

$6.1\textup{ m}$

$5.4\textup{ m}$

The correct answer is not given among the other responses.

$10.7\textup{ m}$

$3.1\textup{ m}$

Correct answer:

$3.1\textup{ m}$

Explanation:

Given the radius , the volume of a sphere is given by the formula

$V = \frac{4}{3} \pi r^{3}$

We find the inner radius by setting V= 120 :

$\frac{4}{3} \pi r^{3} = 120$

$\frac{3}{4} \cdot \frac{4}{3} \pi r^{3} = \frac{3}{4} \cdot 120$

$\pi r^{3} = 90$

$r^{3} =\frac{ 90}{\pi} \approx 28.65$

$r \approx\sqrt[3]{ 28.65} \approx 3.1$ meters.

Report an Error

Example Question #2 : How To Find The Radius Of A Sphere

A spherical balloon is filled with 10,000 cubic meters of gas in the morning when the temperature is $10^{\circ }C$ . The temperature increases to $25^{\circ }C$ by noon, with no other conditions changing. What is the radius of the balloon at noon, to the nearest tenth of a meter?

Possible Answers:

$9.8\textup { m}$

$13.1\textup{ m}$

None of the other responses gives the correct answer.

$18.1\textup{ m}$

$13.6 \textup{ m}$

Correct answer:

$13.6 \textup{ m}$

Explanation:

First, we use the variation equation to figure out the volume of the balloon at noon. First, we add 273 to each of the temperatures.

The initial temperature is $273 + 10 = 283 \textup{ K}$

The final (noon) temperature is $273 + 25= 298 \textup{ K}$

Since volume varies directly as temperature, we can set up the equation

$\frac{V'}{T'} = \frac{V}{T}$

$\frac{V'}{298} = \frac{10,000}{283}$

$V' = \frac{10,000}{283} \cdot 298 \approx 10,530$

The volume of a sphere is given by the formula

$V = \frac{4}{3} \pi r^{3}$

so set V = 10,530 and solve for :

$\frac{4}{3} \pi r^{3} = 10,530$

$\frac{3}{4} \cdot \frac{4}{3} \pi r^{3} = \frac{3}{4} \cdot 10,530$

$\pi r^{3} \approx 7,897.5$

$r^{3} \approx 7,897.5 \div \pi \approx 2,513.8$

$r \approx\sqrt[3]{ 2,513.8} \approx 13.6$ meters.

Report an Error

Example Question #3 : How To Find The Radius Of A Sphere

Find the radius of a sphere whose volume is $\small \small 36\pi$ $\text{in}^3$ .

Possible Answers:

$\small 9$ $\text{in}$

$\small 9\pi$ $\text{in}$

$\small 3\pi$ $\text{in}$

$\small 3$ $\text{in}$

Correct answer:

$\small 3$ $\text{in}$

Explanation:

Use the equation for the volume of a sphere to find the radius.

$\small V = \frac{4}{3}\pi r^{3}$

$\small 36\pi = \frac{4}{3}\pi r^{3}$

$\small \small 36 = \frac{4}{3} r^{3}$

$\small 27 = r^{3}$

$\small r = 3$

So, the radius of the sphere is 3

Report an Error

Example Question #4 : How To Find The Radius Of A Sphere

If a sphere has a volume of $36\pi\textup{ cubic inches}$ , then what is the radius of the sphere?

Possible Answers:

$6\textup{ in}$

$4.5\textup{ in}$

$3\textup{ in}$

$9\textup{ in}$

$18\textup{ in}$

Correct answer:

$3\textup{ in}$

Explanation:

The volume of a sphere is equal to

$v=\left ( \frac{4}{3} \right )\pi r^3$

Therefore,

$r=\sqrt[3]{(3/4)v/\pi}=\sqrt[3]{(3/4)36\pi/\pi}=\sqrt[3]{27}=3$

Report an Error

View PSAT Mathematics Tutors

Keith
Certified Tutor

Xavier University, Bachelor in Business Administration, Accounting. Ohio University-Main Campus, Masters in Education, Mathem...

View PSAT Mathematics Tutors

Crystal
Certified Tutor

SUNY at Binghamton, Bachelor of Science, Mechanical Engineering.

View PSAT Mathematics Tutors

Dr. Derrick
Certified Tutor

Huston-Tillotson University, Bachelor of Science, Mathematics. Grand Canyon University, Master of Arts, Education.

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in Chicago, Computer Science Tutors in Philadelphia, SAT Tutors in Seattle, LSAT Tutors in Phoenix, French Tutors in Atlanta, Math Tutors in San Diego, GMAT Tutors in Phoenix, Physics Tutors in Seattle, SSAT Tutors in Washington DC, Physics Tutors in Los Angeles

Popular Courses & Classes

GMAT Courses & Classes in Denver, ACT Courses & Classes in Seattle, ACT Courses & Classes in Atlanta, LSAT Courses & Classes in Denver, SAT Courses & Classes in Seattle, ACT Courses & Classes in Washington DC, MCAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in New York City, Spanish Courses & Classes in Houston, ISEE Courses & Classes in Philadelphia

Popular Test Prep

SAT Test Prep in Seattle, GMAT Test Prep in Phoenix, ISEE Test Prep in Miami, GRE Test Prep in New York City, ISEE Test Prep in Los Angeles, SSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Washington DC, SAT Test Prep in Atlanta, SAT Test Prep in Miami, SSAT Test Prep in Miami

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

PSAT Math : Spheres

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #191 : Psat Mathematics

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

Example Question #21 : Spheres

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

Example Question #4 : How To Find The Radius Of A Sphere

Example Question #4 : How To Find The Radius Of A Sphere

Example Question #6 : How To Find The Radius Of A Sphere

Example Question #2 : How To Find The Radius Of A Sphere

Example Question #3 : How To Find The Radius Of A Sphere

Example Question #4 : How To Find The Radius Of A Sphere

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: