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GED Math : Faces and Surface Area

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Example Question #11 : Faces And Surface Area

Find the surface area of a cube with a length of 12in.

Possible Answers:

$1014\text{in}^2$

$144\text{in}^2$

$169\text{in}^2$

$726\text{in}^2$

$864\text{in}^2$

Correct answer:

$864\text{in}^2$

Explanation:

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

$SA = 6 \cdot l \cdot w$

where l is the length, and w is the width of the cube.

Now, we know the length of the cube is 12in. Because it is a cube, all sides are equal. Therefore, the width is also 12in. So, we can substitute. We get

$SA = 6 \cdot 12\text{in} \cdot 12\text{in}$

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

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

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Example Question #131 : 3 Dimensional Geometry

A cube has a height of 8cm. Find the surface area.

Possible Answers:

$512\text{cm}^2$

$256\text{cm}^2$

$448\text{cm}^2$

$576\text{cm}^2$

$384\text{cm}^2$

Correct answer:

$384\text{cm}^2$

Explanation:

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

$SA = 6 \cdot l \cdot w$

where l is the length, and w is the width of the cube.

Now, we know the height of the cube is 8cm. Because it is a cube, all lengths, widths, and heights are the same. Therefore, the length and the width are also 8cm.

Knowing this, we can substitute into the formula. We get

$SA = 6 \cdot 8\text{cm} \cdot 8\text{cm}$

$SA = 6 \cdot 64\text{cm}^2$

$SA = 384\text{cm}^2$

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Example Question #11 : Faces And Surface Area

A sphere has a radius of 5in. Find the surface area.

Possible Answers:

$125\pi \text{ in}^2$

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

$175\pi \text{ in}^2$

$250\pi \text{ in}^2$

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

Correct answer:

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

Explanation:

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

$SA = 4 \cdot \pi \cdot r^2$

where r is the radius of the sphere.

Now, we know the radius of the sphere is 5in.

So, we can substitute into the formula. We get

$SA = 4 \cdot \pi \cdot (5\text{in})^2$

$SA = 4 \cdot \pi \cdot 25\text{in}^2$

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

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

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Example Question #14 : Faces And Surface Area

Find the surface area of a cube with a height of 13in.

Possible Answers:

$144\text{in}^2$

$864\text{in}^2$

$1014\text{in}^2$

$726\text{in}^2$

$169\text{in}^2$

Correct answer:

$1014\text{in}^2$

Explanation:

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

$SA = 6 \cdot l \cdot w$

where l is the length, and w is the width of the cube.

Now, we know the length of the cube is 13in. Because it is a cube, all sides are equal. Therefore, the width is also 13in. So, we can substitute. We get

$SA = 6 \cdot 13\text{in} \cdot 13\text{in}$

$SA = 6 \cdot 169\text{in}^2$

$SA = 1014\text{in}^2$

Report an Error

Example Question #15 : Faces And Surface Area

Find the surface area of a sphere with a radius of 8in.

Possible Answers:

$1024\pi \text{ in}^2$

$512\pi \text{ in}^2$

$384\pi \text{ in}^2$

$64\pi \text{ in}^2$

$256\pi \text{ in}^2$

Correct answer:

$256\pi \text{ in}^2$

Explanation:

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

$SA = 4 \cdot \pi \cdot r^2$

where r is the radius of the sphere.

Now, we know the radius of the sphere is 8in.

Knowing this, we can substitute into the formula. We get

$SA = 4 \cdot \pi \cdot (8\text{in})^2$

$SA = 4 \cdot \pi \cdot 64\text{in}^2$

$SA = 256 \pi \text{ in}^2$

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Example Question #16 : Faces And Surface Area

Sphere

Give the surface area of the above sphere.

Possible Answers:

$28 \pi$

$\frac{28 }{3}\pi$

$28 \pi \sqrt{7}$

$\frac{28 }{3}\pi \sqrt{7}$

Correct answer:

$28 \pi$

Explanation:

Given the radius of a sphere, the surface area can be calculated using the formula

$A = 4 \pi r^{2}$ .

Set $r = \sqrt{7}$ in the formula and evaluate:

$A = 4 \pi ( \sqrt{7})^{2}$

$A = 4 \pi \cdot 7$

$A = 28 \pi$

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Example Question #11 : Faces And Surface Area

A cube has a width of 8in. Find the surface area.

Possible Answers:

$128\text{in}^2$

$512\text{in}^2$

$96\text{in}^2$

$200\text{in}^2$

$384\text{in}^2$

Correct answer:

$384\text{in}^2$

Explanation:

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

$SA = 6 \cdot l \cdot w$

where l is the length, and w is the width of the cube.

Now, we know the width of the cube is 8in. Because it is a cube, all sides/lengths are equal. Therefore, the length is also 8in. So, we can substitute. We get

$SAA = 6 \cdot 8\text{in} \cdot 8\text{in}$

$SA = 6 \cdot 64\text{in}^2$

$SA = 384\text{in}^2$

Report an Error

Example Question #18 : Faces And Surface Area

Let $\pi = 3.14$

Find the surface area of a sphere with a radius of 5in.

Possible Answers:

$62.8\text{in}^2$

$125.6\text{in}^2$

$157\text{in}^2$

$78.5\text{in}^2$

$314\text{in}^2$

Correct answer:

$314\text{in}^2$

Explanation:

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

$SA = 4 \cdot \pi \cdot r^2$

where r is the radius of the sphere.

Now, we know $\pi = 3.14$ . We know the radius of the sphere is 5in. So, we can substitute. We get

$SA = 4 \cdot 3.14 \cdot (5\text{in})^2$

$SA = 4 \cdot 3.14 \cdot 25\text{in}^2$

$SA = 4 \cdot 25\text{in}^2 \cdot 3.14$

$SA = 100\text{in}^2 \cdot 3.14$

$SA = 314\text{in}^2$

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Example Question #19 : Faces And Surface Area

Let $\pi = 3.14$

If a sphere has a radius of 3cm, find the surface area.

Possible Answers:

$339.12\text{cm}^2$

$75.36\text{cm}^2$

$18.84\text{cm}^2$

$37.68\text{cm}^2$

$113.04\text{cm}^2$

Correct answer:

$113.04\text{cm}^2$

Explanation:

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

$SA = 4 \cdot \pi \cdot r^2$

where r is the radius of the sphere.

Now, we know $\pi = 3.14$ . We know the radius of the sphere is 3cm. So, we substitute. We get

$SA = 4 \cdot 3.14 \cdot (3\text{cm})^2$

$SA = 4 \cdot 3.14 \cdot 9\text{cm}^2$

$SA = 4 \cdot 9\text{cm}^2 \cdot 3.14$

$SA = 36\text{cm}^2 \cdot 3.14$

$SA = 113.04\text{cm}^2$

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Example Question #20 : Faces And Surface Area

Find the surface area of a cube with a length of 9in.

Possible Answers:

$384\text{in}^2$

$486\text{in}^2$

$729\text{in}^2$

$108\text{in}^2$

$324\text{in}^2$

Correct answer:

$486\text{in}^2$

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 length of the cube is 9in. Because it is a cube, all sides/lengths are equal. Therefore, we can use any side of the cube in the formula. So, we get

$SA = 6 \cdot (9\text{in})^2$

$SA = 6 \cdot 81\text{in}^2$

$SA = 486\text{in}^2$

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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 #11 : Faces And Surface Area

Example Question #131 : 3 Dimensional Geometry

Example Question #11 : Faces And Surface Area

Example Question #14 : Faces And Surface Area

Example Question #15 : Faces And Surface Area

Example Question #16 : Faces And Surface Area

Example Question #11 : Faces And Surface Area

Example Question #18 : Faces And Surface Area

Example Question #19 : Faces And Surface Area

Example Question #20 : Faces And Surface Area

All GED Math Resources

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