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GED Math : GED Math

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

Example Questions

Example Question #1661 : Ged Math

Let $\pi = 3.14$ $\displaystyle \pi = 3.14$

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

Possible Answers:

$78.5\text{in}^2$ $\displaystyle 78.5\text{in}^2$

$62.8\text{in}^2$ $\displaystyle 62.8\text{in}^2$

$314\text{in}^2$ $\displaystyle 314\text{in}^2$

$157\text{in}^2$ $\displaystyle 157\text{in}^2$

$125.6\text{in}^2$ $\displaystyle 125.6\text{in}^2$

Correct answer:

$314\text{in}^2$ $\displaystyle 314\text{in}^2$

Explanation:

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

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

where r is the radius of the sphere.

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

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

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

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

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

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

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Example Question #691 : Geometry And Graphs

Let $\pi = 3.14$ $\displaystyle \pi = 3.14$

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

Possible Answers:

$75.36\text{cm}^2$ $\displaystyle 75.36\text{cm}^2$

$37.68\text{cm}^2$ $\displaystyle 37.68\text{cm}^2$

$339.12\text{cm}^2$ $\displaystyle 339.12\text{cm}^2$

$18.84\text{cm}^2$ $\displaystyle 18.84\text{cm}^2$

$113.04\text{cm}^2$ $\displaystyle 113.04\text{cm}^2$

Correct answer:

$113.04\text{cm}^2$ $\displaystyle 113.04\text{cm}^2$

Explanation:

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

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

where r is the radius of the sphere.

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

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

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

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

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

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

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Example Question #692 : Geometry And Graphs

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

Possible Answers:

$729\text{in}^2$ $\displaystyle 729\text{in}^2$

$324\text{in}^2$ $\displaystyle 324\text{in}^2$

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

$108\text{in}^2$ $\displaystyle 108\text{in}^2$

$486\text{in}^2$ $\displaystyle 486\text{in}^2$

Correct answer:

$486\text{in}^2$ $\displaystyle 486\text{in}^2$

Explanation:

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

$\displaystyle SA = 6a^2$

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

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

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

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

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Example Question #691 : Geometry And Graphs

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

Possible Answers:

$9\pi^4$ $\displaystyle 9\pi^4$

$18\pi$ $\displaystyle 18\pi$

$27\pi^2$ $\displaystyle 27\pi^2$

$54 \pi ^2$ $\displaystyle 54 \pi ^2$

$9\pi^2$ $\displaystyle 9\pi^2$

Correct answer:

$54 \pi ^2$ $\displaystyle 54 \pi ^2$

Explanation:

Write the formula for the surface area of a cube.

A =6s^2 $\displaystyle A =6s^2$

Substitute the side length into the formula.

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

The answer is: $54 \pi ^2$ $\displaystyle 54 \pi ^2$

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Example Question #1661 : Ged Math

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

Possible Answers:

108 $\displaystyle 108$

$36\sqrt2$ $\displaystyle 36\sqrt2$

$\displaystyle 72$

$18\sqrt2$ $\displaystyle 18\sqrt2$

$\displaystyle 36$

Correct answer:

108 $\displaystyle 108$

Explanation:

Write the formula for the surface area of a cube.

A =6s^2 $\displaystyle A =6s^2$

Substitute the side.

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

The answer is: 108 $\displaystyle 108$

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Example Question #21 : Faces And Surface Area

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

Possible Answers:

$1728\text{in}^2$ $\displaystyle 1728\text{in}^2$

$864\text{in}^2$ $\displaystyle 864\text{in}^2$

$144\text{in}^2$ $\displaystyle 144\text{in}^2$

$576\text{in}^2$ $\displaystyle 576\text{in}^2$

$720\text{in}^2$ $\displaystyle 720\text{in}^2$

Correct answer:

$864\text{in}^2$ $\displaystyle 864\text{in}^2$

Explanation:

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

$\displaystyle SA = 6a^2$

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

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

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

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

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Example Question #701 : Geometry And Graphs

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

Possible Answers:

$44\text{in}^2$ $\displaystyle 44\text{in}^2$

$66\text{in}^2$ $\displaystyle 66\text{in}^2$

$726\text{in}^2$ $\displaystyle 726\text{in}^2$

$484\text{in}^2$ $\displaystyle 484\text{in}^2$

$121\text{in}^2$ $\displaystyle 121\text{in}^2$

Correct answer:

$726\text{in}^2$ $\displaystyle 726\text{in}^2$

Explanation:

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

$\displaystyle SA = 6a^2$

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

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

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

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

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Example Question #151 : 3 Dimensional Geometry

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

where r is the radius of the sphere.

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

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

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

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

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

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

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Example Question #701 : Geometry And Graphs

Find the surface area of a cube with a side edge of $\displaystyle 8x$.

Possible Answers:

64x^4 $\displaystyle 64x^4$

384 x^2 $\displaystyle 384 x^2$

48x^2 $\displaystyle 48x^2$

196x^2 $\displaystyle 196x^2$

64x^2 $\displaystyle 64x^2$

Correct answer:

384 x^2 $\displaystyle 384 x^2$

Explanation:

Write the formula for the surface area of a cube.

A= 6s^2 $\displaystyle A= 6s^2$

Substitute the side into the equation.

$\displaystyle A= 6(8x)^2 = 6(8x)(8x) = 384x^2$

The answer is: 384 x^2 $\displaystyle 384 x^2$

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Example Question #22 : Faces And Surface Area

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

Possible Answers:

214 $\displaystyle 214$

216 $\displaystyle 216$

252 $\displaystyle 252$

1296 $\displaystyle 1296$

Correct answer:

216 $\displaystyle 216$

Explanation:

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

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

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

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

$\text{side}^2=36$ $\displaystyle \text{side}^2=36$

$\text{side}=6$ $\displaystyle \text{side}=6$

Now recall how to find the volume of a cube:

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

Plug in the found side length to find the volume.

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

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1661 : Ged Math

Example Question #691 : Geometry And Graphs

Example Question #692 : Geometry And Graphs

Example Question #691 : Geometry And Graphs

Example Question #1661 : Ged Math

Example Question #21 : Faces And Surface Area

Example Question #701 : Geometry And Graphs

Example Question #151 : 3 Dimensional Geometry

Example Question #701 : Geometry And Graphs

Example Question #22 : Faces And Surface Area

All GED Math Resources

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