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GED Math : 3-Dimensional Geometry

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #141 : 3 Dimensional Geometry

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

Possible Answers:

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

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

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

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

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

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 #142 : 3 Dimensional Geometry

Sphere

Give the surface area of the above sphere.

Possible Answers:

$28 \pi \sqrt{7}$

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

$28 \pi$

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

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 #692 : Geometry And Graphs

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

Possible Answers:

$200\text{in}^2$

$128\text{in}^2$

$384\text{in}^2$

$96\text{in}^2$

$512\text{in}^2$

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

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

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

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

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Example Question #693 : Geometry And Graphs

Let $\pi = 3.14$

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

Possible Answers:

$157\text{in}^2$

$78.5\text{in}^2$

$62.8\text{in}^2$

$314\text{in}^2$

$125.6\text{in}^2$

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 #1661 : Ged Math

Let $\pi = 3.14$

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

Possible Answers:

$37.68\text{cm}^2$

$339.12\text{cm}^2$

$75.36\text{cm}^2$

$18.84\text{cm}^2$

$113.04\text{cm}^2$

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 #142 : 3 Dimensional Geometry

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

Possible Answers:

$384\text{in}^2$

$486\text{in}^2$

$108\text{in}^2$

$729\text{in}^2$

$324\text{in}^2$

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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Example Question #691 : Geometry And Graphs

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

Possible Answers:

$18\pi$

$54 \pi ^2$

$27\pi^2$

$9\pi^2$

$9\pi^4$

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 #697 : Geometry And Graphs

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

Possible Answers:

108

$36\sqrt2$

$18\sqrt2$

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 #21 : Faces And Surface Area

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

Possible Answers:

$1728\text{in}^2$

$864\text{in}^2$

$144\text{in}^2$

$576\text{in}^2$

$720\text{in}^2$

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 #701 : Geometry And Graphs

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

Possible Answers:

$484\text{in}^2$

$121\text{in}^2$

$66\text{in}^2$

$44\text{in}^2$

$726\text{in}^2$

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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GED Math : 3-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #141 : 3 Dimensional Geometry

Example Question #142 : 3 Dimensional Geometry

Example Question #692 : Geometry And Graphs

Example Question #693 : Geometry And Graphs

Example Question #1661 : Ged Math

Example Question #142 : 3 Dimensional Geometry

Example Question #691 : Geometry And Graphs

Example Question #697 : Geometry And Graphs

Example Question #21 : Faces And Surface Area

Example Question #701 : Geometry And Graphs

All GED Math Resources

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