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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 #132 : 3 Dimensional Geometry

A regular tetrahedron has four congruent faces, each of which is an equilateral triangle.

A given tetrahedron has edges of length five inches. Give the total surface area of the tetrahedron.

Possible Answers:

$25 \sqrt{3}\textrm{ in}^{2}$

$\frac{25\sqrt{3}}{2} \textrm{ in}^{2}$

$\frac{25\sqrt{2}}{2} \textrm{ in}^{2}$

$25 \sqrt{2}\textrm{ in}^{2}$

Correct answer:

$25 \sqrt{3}\textrm{ in}^{2}$

Explanation:

The area of an equilateral triangle is given by the formula

$A = \frac{s^{2}\sqrt{3}}{4}$ .

Since there are four equilateral triangles that comprise the surface of the tetrahedron, the total surface area is

$SA = 4 A = 4 \cdot \frac{s^{2}\sqrt{3}}{4} = s^{2}\sqrt{3}$ .

Substitute s = 5 :

$SA = 5^{2}\sqrt{3} = 25 \sqrt{3}$ square inches.

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Example Question #1651 : Ged Math

A cube has a height of 9cm. Find the surface area.

Possible Answers:

$108\text{cm}^2$

$405\text{cm}^2$

$729\text{cm}^2$

$324\text{cm}^2$

$486\text{cm}^2$

Correct answer:

$486\text{cm}^2$

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 9cm. Because it is a cube, all lengths, widths, and heights are the same. Therefore, the length and the width are also 9cm.

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

$SA = 6 \cdot 9\text{cm} \cdot 9\text{cm}$

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

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

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Example Question #1652 : Ged Math

A sphere has a radius of 7in. Find the surface area.

Possible Answers:

$56\pi \text{ in}^2$

$294\pi \text{ in}^2$

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

$196\pi \text{ in}^2$

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

Correct answer:

$196\pi \text{ in}^2$

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 7in.

So, we can substitute into the formula. We get

$SA = 4 \cdot \pi \cdot (7\text{in})^2$

$SA = 4 \cdot \pi \cdot 49\text{in}^2$

$SA = 196\text{in}^2 \cdot \pi$

$SA = 196\pi \text{ in}^2$

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Example Question #681 : Geometry And Graphs

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

Possible Answers:

$1014\text{in}^2$

$864\text{in}^2$

$169\text{in}^2$

$726\text{in}^2$

$144\text{in}^2$

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 #1653 : Ged Math

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

Possible Answers:

$256\text{cm}^2$

$384\text{cm}^2$

$512\text{cm}^2$

$576\text{cm}^2$

$448\text{cm}^2$

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 #132 : 3 Dimensional Geometry

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

Possible Answers:

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

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

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

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

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

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 #1654 : Ged Math

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

Possible Answers:

$1014\text{in}^2$

$864\text{in}^2$

$169\text{in}^2$

$726\text{in}^2$

$144\text{in}^2$

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

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

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

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

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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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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #132 : 3 Dimensional Geometry

Example Question #1651 : Ged Math

Example Question #1652 : Ged Math

Example Question #681 : Geometry And Graphs

Example Question #1653 : Ged Math

Example Question #132 : 3 Dimensional Geometry

Example Question #1654 : Ged Math

Example Question #141 : 3 Dimensional Geometry

Example Question #142 : 3 Dimensional Geometry

Example Question #692 : Geometry And Graphs

All GED Math Resources

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