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GED Math : 3-Dimensional Geometry

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Example Questions

Example Question #5 : Faces And Surface Area

Cone_1

Above is a diagram of a conic tank that holds a city's water supply.

The city wishes to completely repaint the exterior of the tank - sides and base. The paint it wants to use covers 40 square meters per gallon. Also, to save money, the city buys the paint in multiples of 25 gallons.

How many gallons will the city purchase in order to paint the tower?

Possible Answers:

1,450

275

975

375

Correct answer:

375

Explanation:

The surface area of a cone with radius and slant height is calculated using the formula $S = \pi r^{2} + \pi r l$ .

Substitute 35 for and 100 for to find the surface area in square meters:

$S = \pi \cdot 35^{2} + \pi \cdot 35 \cdot 100$

$\approx 3.14 \cdot 1,225 + 3.14\cdot 35 \cdot 100$

$\approx 3,848 + 10,996$

$\approx 14,844$ square meters.

The paint covers 40 square meters per gallon, so the city needs

$14,844 \div 40 =371.1$ gallons of paint.

Since the city buys the paint in multiples of 25 gallons, it will need to buy the next-highest multiple of 25, or 375 gallons.

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Example Question #131 : 3 Dimensional Geometry

A regular octahedron has eight congruent faces, each of which is an equilateral triangle.

A given octahedron has edges of length three inches. Give the total surface area of the octahedron.

Possible Answers:

$9\sqrt{3} \textrm{ in}^{2}$

$18\sqrt{3} \textrm{ in}^{2}$

$18\sqrt{2} \textrm{ in}^{2}$

$9\sqrt{2} \textrm{ in}^{2}$

Correct answer:

$18\sqrt{3} \textrm{ in}^{2}$

Explanation:

The area of an equilateral triangle is given by the formula

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

Since there are eight equilateral triangles that comprise the surface of the octahedron, the total surface area is

$SA = 8 A = 8 \cdot \frac{s^{2}\sqrt{3}}{4} = 2 s^{2}\sqrt{3}$ .

Substitute s = 3 :

$SA =2 \cdot 3^{2}\sqrt{3} = 18 \sqrt{3}$ square inches.

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Example Question #1645 : Ged Math

A regular icosahedron has twenty congruent faces, each of which is an equilateral triangle.

A given regular icosahedron has edges of length two inches. Give the total surface area of the icosahedron.

Possible Answers:

$10 \sqrt{2} \textrm{ in}^{2}$

$20 \sqrt{2} \textrm{ in}^{2}$

$20 \sqrt{3} \textrm{ in}^{2}$

$10 \sqrt{3} \textrm{ in}^{2}$

Correct answer:

$20 \sqrt{3} \textrm{ in}^{2}$

Explanation:

The area of an equilateral triangle is given by the formula

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

Since there are twenty equilateral triangles that comprise the surface of the icosahedron, the total surface area is

$SA = 20 A = 20 \cdot \frac{s^{2}\sqrt{3}}{4} = 5 s^{2}\sqrt{3}$ .

Substitute s = 2 :

$SA = 5 \cdot 2^{2}\sqrt{3} = 5 \cdot 4 \sqrt{3} = 20 \sqrt{3}$ square inches.

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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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GED Math : 3-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #5 : Faces And Surface Area

Example Question #131 : 3 Dimensional Geometry

Example Question #1645 : Ged Math

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

All GED Math Resources

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