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GED Math : Faces and Surface Area

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Example Question #21 : Faces And Surface Area

Find the surface area of a cube with a side length of $3\pi$ .

Possible Answers:

$9\pi^4$

$54 \pi ^2$

$18\pi$

$27\pi^2$

$9\pi^2$

Correct answer:

$54 \pi ^2$

Explanation:

Write the formula for the surface area of a cube.

A =6s^2

Substitute the side length into the formula.

$A =6(3\pi)^2 = 6(9\pi ^2)$

The answer is: $54 \pi ^2$

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Example Question #692 : Geometry And Graphs

Find the surface area of a cube with a side length of $3\sqrt2$ .

Possible Answers:

$18\sqrt2$

108

$36\sqrt2$

Correct answer:

108

Explanation:

Write the formula for the surface area of a cube.

A =6s^2

Substitute the side.

$A =6(3\sqrt2)^2=6(3\sqrt2)(3\sqrt2) = 6(9)(2)$

The answer is: 108

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Example Question #701 : Geometry And Graphs

A cube has a height of 12in. Find the surface area.

Possible Answers:

$144\text{in}^2$

$864\text{in}^2$

$576\text{in}^2$

$720\text{in}^2$

$1728\text{in}^2$

Correct answer:

$864\text{in}^2$

Explanation:

To find the surface area of a cube, we will use the following formula.

SA = 6a^2

where a is the length of any side of the cube.

Now, we know the height of the cube is 12in. Because it is a cube, all sides are equal (this is why we can use any length/side in the formula). So, we will use 12in in the formula. We get

$SA = 6 \cdot (12\text{in})^2$

$SA = 6 \cdot 144\text{in}^2$

$SA = 864\text{in}^2$

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Example Question #702 : Geometry And Graphs

Find the surface area of a cube with a length of 11in.

Possible Answers:

$726\text{in}^2$

$44\text{in}^2$

$121\text{in}^2$

$484\text{in}^2$

$66\text{in}^2$

Correct answer:

$726\text{in}^2$

Explanation:

To find the surface area of a cube, we will use the following formula:

SA = 6a^2

where a is any length of the cube. Because a cube has equal lengths, widths, heights, we can use any of those sides in the formula.

Now, we know the length of the cube is 11in. So, we can substitute. We get

$SA = 6 \cdot (11\text{in})^2$

$SA = 6 \cdot 121\text{in}^2$

$SA = 726\text{in}^2$

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Example Question #22 : Faces And Surface Area

Find the surface area of a sphere with a radius of 10in.

Possible Answers:

$100\pi \text{ in}^2$

$40\pi \text{ in}^2$

$75\pi \text{ in}^2$

$400\pi \text{ in}^2$

$25\pi \text{ in}^2$

Correct answer:

$400\pi \text{ in}^2$

Explanation:

To find the surface area of a sphere, we will use the following formula:

$SA = 4\pi r^2$

where r is the radius of the sphere.

Now, we know the radius of the sphere is 10in. So, we will substitute. We get

$SA = 4 \cdot \pi \cdot (10\text{in})^2$

$SA = 4 \cdot \pi \cdot 100\text{in}^2$

$SA = 4 \cdot 100\text{in}^2 \cdot \pi$

$SA = 400\text{in}^2 \cdot \pi$

$SA = 400\pi \text{ in}^2$

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Example Question #23 : Faces And Surface Area

Find the surface area of a cube with a side edge of .

Possible Answers:

64x^2

196x^2

384 x^2

48x^2

64x^4

Correct answer:

384 x^2

Explanation:

Write the formula for the surface area of a cube.

A= 6s^2

Substitute the side into the equation.

A= 6(8x)^2 = 6(8x)(8x) = 384x^2

The answer is: 384 x^2

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Example Question #705 : Geometry And Graphs

If the surface area of a cube is 216 in^2 , what is the volume of the cube in cubic inches?

Possible Answers:

214

216

252

1296

Correct answer:

216

Explanation:

Recall the formula to find the surface area of a cube:

$\text{Surface Area}=6(\text{side})^2$

Start by solving for the length of a side of the cube.

$216=6(\text{side})^2$

$\text{side}^2=36$

$\text{side}=6$

Now recall how to find the volume of a cube:

$\text{Volume}=\text{side}^3$

Plug in the found side length to find the volume.

$\text{Volume}=6^3=216$

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Example Question #706 : Geometry And Graphs

Find the surface area of the square with a side length of $3\sqrt3$ .

Possible Answers:

$36\sqrt3$

$96\sqrt3$

162

Correct answer:

162

Explanation:

Write the formula for the surface area of a square.

A= 6s^2

We will determine the areas of the 6 faces of the square.

$A= 6(3\sqrt3)^2=6(3\sqrt3)(3\sqrt3) = 6(3(3(3))) = 162$

The answer is: 162

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Example Question #707 : Geometry And Graphs

You are given a small cube with an edge length of . Find the surface area of the cube.

Possible Answers:

27cm^2

18cm^2

63cm^2

54cm^2

Correct answer:

54cm^2

Explanation:

You are given a small cube with an edge length of . Find the surface area of the cube.

A cube has six faces, each with an area of side squared. Thus, we use the formula:

SA=6s^2

Now, we plug in our side length and solve.

SA=6(3cm)^2=6*9cm^2=54cm^2

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Example Question #151 : 3 Dimensional Geometry

You are given a chest with the following dimensions: 3' X 2' X 1.5'.

What is the surface area of the chest?

Possible Answers:

9ft^2

27ft^2

25ft^2

18.5ft^2

Correct answer:

27ft^2

Explanation:

You are given a chest with the following dimensions: 3' X 2' X 1.5'.

What is the surface area of the chest?

To find the surface area of a rectangular prism, use the following formula:

SA=2lw+2hw+2lh

Where l, h and w are length, width and height.

So, let's plug in our values and solve for SA.

SA=(2(3*2)+2(2*1.5)+2(3*1.5))ft^2=(12+6+9)ft^2=27ft^2

So, our answer is

27ft^2

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GED Math : Faces and Surface Area

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #21 : Faces And Surface Area

Example Question #692 : Geometry And Graphs

Example Question #701 : Geometry And Graphs

Example Question #702 : Geometry And Graphs

Example Question #22 : Faces And Surface Area

Example Question #23 : Faces And Surface Area

Example Question #705 : Geometry And Graphs

Example Question #706 : Geometry And Graphs

Example Question #707 : Geometry And Graphs

Example Question #151 : 3 Dimensional Geometry

All GED Math Resources

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