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High School Math : Geometry

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Example Questions

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

A cube has a height of 4 feet. What is the surface area of the cube in feet?

Possible Answers:

Correct answer:

Explanation:

To find the surface area of a cube, square the length of one edge and multiply the result by six: $6(a^{2})$

$6(4^{2})=6(16)=96$

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Example Question #16 : Cubes

The side length of a particular cube is $\frac{3}{2}$ . What is the surface area of this cube?

Possible Answers:

$\frac{27}{2}$

$\frac{9}{2}$

Correct answer:

$\frac{27}{2}$

Explanation:

To find the surface of a cube, use the standard equation:

SA=6a^2

where denotes the side length.

Plug in the given value for to find the answer:

$SA=6\cdot \left(\frac{3}{2}\right)^2=6\cdot \left(\frac{9}{4}\right)=\frac{27}{2}$

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Example Question #17 : Cubes

Sarah is wrapping a birthday present. The box is a cube with sides of $6\; in$ . At a minimum, how many square feet of wrapping paper will she need?

Possible Answers:

$1.00\; ft^{2}$

$1.50\; ft^{2}$

$0.75\; ft^{2}$

$1.25\; ft^{2}$

$0.50\; ft^{2}$

Correct answer:

$1.50\; ft^{2}$

Explanation:

Remember, $6\; in=0.50\; ft$ .

For a cube:

$SA = 6s^{2}$

Thus $6(0.50)^{2}=6(0.25)=1.50\; ft^{2}$ .

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Example Question #41 : Solid Geometry

$\textup{What is the surface area, in terms of }p,\textup{of a cube with sides of length }p\textup{ ?}$

Possible Answers:

$4p^{2}$

$6p^{2}$

$p^{2}$

$p^{3}$

12p

Correct answer:

$6p^{2}$

Explanation:

$\textup{Each of the six identical faces of the cube is a square with sides }p.$

$\textup{Each face: }A=p^{2}\: \: \: \: \: \textup{Surface area}=6p^{2}$

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Example Question #42 : Solid Geometry

Find the surface area of the following cube:

Length_of_diagonal

Possible Answers:

$80\ m^2$

$88\ m^2$

$90\ m^2$

$96\ m^2$

$82\ m^2$

Correct answer:

$96\ m^2$

Explanation:

The formula for the surface area of a cube is

SA=6(s)^2 ,

where is the length of the side.

Plugging in our values, we get:

$SA=6(4\ m)^2$

$SA=96\ m^2$

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

The side of a cube has a length of $\dpi{100} \small 5 cm$ . What is the total surface area of the cube?

Possible Answers:

$\dpi{100} \small 125 cm^{2}$

$\dpi{100} \small 5cm^{2}$

$\dpi{100} \small 150cm^{2}$

$\dpi{100} \small 25 cm^{2}$

$\dpi{100} \small 50 cm^{2}$

Correct answer:

$\dpi{100} \small 150cm^{2}$

Explanation:

A cube has 6 faces. The area of each face is found by squaring the length of the side.

$\dpi{100} \small 5\times 5 = 25$

Multiply the area of one face by the number of faces to get the total surface area of the cube.

$\dpi{100} \small 25 \times 6=150$

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

What is the surface area of a cube if its height is 3 cm?

Possible Answers:

$25\ cm^2$

$36\ cm^2$

$45\ cm^2$

$54\ cm^2$

$63\ cm^2$

Correct answer:

$54\ cm^2$

Explanation:

The area of one face is given by the length of a side squared.

$A_{face}=(3cm)^2=9\ cm^2$

The area of 6 faces is then given by six times the area of one face: 54 cm².

$A_{total}=6(A_{face})=6(9\ cm^2)=54\ cm^2$

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Example Question #583 : Geometry

A sphere with a volume of $\frac{32}{3}$ $\pi m^{3}$ is inscribed in a cube, as shown in the diagram below.

Act4

What is the surface area of the cube, in $m^{2}$ ?

Possible Answers:

$24\ m^{2}$

$48\pi \ m^{2}$

$96\ m^{2}$

$48\ m^{2}$

$48\pi ^{2}\ m^{2}$

Correct answer:

$96\ m^{2}$

Explanation:

We must first find the radius of the sphere in order to solve this problem. Since we already know the volume, we will use the volume formula to do this.

$V_{sphere}=\frac{4}{3}\pi r^{3}$

$\frac{32}{3}\pi =\frac{4}{3}\pi r^{3}$

$\frac{32}{3}=\frac{4}{3}r^{3}$

$\frac{3}{4}\cdot \frac{32}{3}= r^{3}$

$8=r^{3}$

r=2

With the radius of the sphere in hand, we can now apply it to the cube. The radius of the sphere is half the distance from the top to the bottom of the cube (or half the distance from one side to another). Therefore, the radius represents half of a side length of a square. So in this case

$side=2\cdot 2=4$

The formula for the surface area of a cube is:

$SA_{cube}=6s^{2}$

$6s^{2}=6\cdot (4)^{2}=6\cdot 16=96$

The surface area of the cube is $96\ m^{2}$

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Example Question #22 : Cubes

If a right triangle has a hypotenuse of length 5, and the length of the other sides are and , what would be the surface area of a cube having side length ?

Possible Answers:

$5\sqrt{5}$

None of these answers.

$25\sqrt{5}$

Correct answer:

Explanation:

By the Pythagorean Theorem,

x^2 + (2x)^2 = 5^2

x^2 + 4x^2 = 25

5x^2 = 25

x^2 = 5

$x=\sqrt{5}$

The surface area of a cube having 6 sides, is 6 times the area of one of its sides.

The area of any side of a cube is the square of the side length.

So if the side length is , the area of any side is x^2 , or .

Thus the surface area of the cube is

6*(5)

=30

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

A box measures $11 \ cm \times 10 \ cm \times 8 \ cm$ . How many dice can fit in this box if the dice are cubes with sides of length $2 \ cm$ ?

Possible Answers:

100 dice

880 dice

110 dice

dice

800 dice

Correct answer:

100 dice

Explanation:

Since the dice are $2 \ cm$ on each of their sides, of them would measure $10 \ cm$ in length when standing face-to-face. This means dice will fit along the edge of the box that measures $10 \ cm$ .

dice will also fit on the edge of the box measuring $11 \ cm$ , but will not fit since adding an additional die would bring the length of the dice standing face-to-face up to $12 \ cm$ . There are no half-dice to fill the gap, so there is a small empty space on this side.

dice will fit along the side that measures $8 \ cm$ .

Treating "dice" as the unit of measurement instead of and considering only the volume where the dice will fit, one ends up with a rectangular shape measuring dice $\times$ dice $\times$ dice. The volume of this shape is the number of dice that will fit in this area (and thus the box). Find the volume by multiplying all lengths of the shape's sides together:

$5 \times 5 \times 4$ dice = 100 dice.

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High School Math : Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

Example Question #16 : Cubes

Example Question #17 : Cubes

Example Question #41 : Solid Geometry

Example Question #42 : Solid Geometry

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

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

Example Question #583 : Geometry

Example Question #22 : Cubes

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

All High School Math Resources

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