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HSPT Math : Geometry

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Example Questions

Example Question #93 : Solid Geometry

What is the surface area of a hemisphere with a diameter of $4\ cm$ ?

Possible Answers:

$12\pi \ cm^{2}$

$20\pi \ cm^{2}$

$8\pi \ cm^{2}$

$16\pi \ cm^{2}$

$18\pi \ cm^{2}$

Correct answer:

$12\pi \ cm^{2}$

Explanation:

A hemisphere is half of a sphere. The surface area is broken into two parts: the spherical part and the circular base.

The surface area of a sphere is given by $SA = 4\pi r^{2}$ .

So the surface area of the spherical part of a hemisphere is $SA = 2\pi r^{2}$ .

The area of the circular base is given by $A = \pi r^{2}$ . The radius to use is half the diameter, or 2 cm.

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Example Question #21 : How To Find Surface Area

Find the surface area of a sphere with a radius of $10\textup{ units}$ .

Possible Answers:

$10\pi$

$400 \pi$

$40\pi$

$14\pi$

$100\pi$

Correct answer:

$400 \pi$

Explanation:

Write the surface area formula for a sphere.

$A=4\pi r^2$

Substitute the value of the radius.

$A=4\pi r^2= 4\pi (10)^2 = 400 \pi$

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Example Question #22 : How To Find Surface Area

Find the surface area of a cube with a side length of .

Possible Answers:

760

100

600

Correct answer:

600

Explanation:

Write the formula for the surface area of a cube.

S=6s^2

Substitute the length.

S=6(10)^2= 600

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Example Question #341 : Geometry

What is the surface area of a cube with a side length of three?

Possible Answers:

108

Correct answer:

Explanation:

Write the formula for the surface area of a cube.

A= 6s^2

Substitute the side length into the equation.

A= 6(3)^2

Simplify the square inside the parentheses and multiply.

$A= 6(3)^2 = 6\times 9= 54$

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Example Question #24 : How To Find Surface Area

Find the surface area of a cube with side length .

Possible Answers:

4x^2

24x^2

16x^2

8x^3

Correct answer:

24x^2

Explanation:

To solve, simply use the following formula for the surface area of a cube.

Thus,

$\\SA=6s^2\\SA=6*(2x)^2\\SA=6*4x^2\\SA=24x^2$

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Example Question #25 : How To Find Surface Area

If a cube has an area of on one of its sides, what is the total surface area?

Possible Answers:

125

150

200

100

Correct answer:

150

Explanation:

A cube has sides that have equal length edges and also equal side areas.

To find the total surface area, you just need to multiple the side area () by which is,

$\\SA=6\cdot A \\SA=6\cdot 25 \\SA=150$ .

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Example Question #26 : How To Find Surface Area

A sphere has diameter 12. What is 75% of its surface area?

Possible Answers:

$432 \pi$

$216 \pi$

$108 \pi$

$1,728 \pi$

Correct answer:

$108 \pi$

Explanation:

The radius of a sphere is half its diameter, which here is 12, so the radius is 6. The surface area of the sphere can be calculated by setting r = 6 in the formula:

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

$A = 4 \pi \cdot 6^{2}$

$A = 4 \pi \cdot 36$

$A = 144 \pi$

75% of this is

$144 \pi \cdot \frac{75}{100} = 108 \pi$

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Example Question #27 : How To Find Surface Area

Cylinder

Which expression is equal to 40% of the surface area of the above cylinder?

Possible Answers:

$800 \pi$

$4,800 \pi$

$2,500 \pi$

$30,000 \pi$

Correct answer:

$800 \pi$

Explanation:

The surface area of the cylinder can be calculated by setting r = 20 and h = 30 in the formula

$A =2 \pi r (r + h)$

$A =2 \pi \cdot 20 (20 + 30)$

$A =2 \pi \cdot 20 \cdot 50$

$A = 2,000 \pi$

40% of this surface area is

$2 ,000 \pi \cdot \frac{40}{100} = 800 \pi$

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HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #93 : Solid Geometry

Example Question #21 : How To Find Surface Area

Example Question #22 : How To Find Surface Area

Example Question #341 : Geometry

Example Question #24 : How To Find Surface Area

Example Question #25 : How To Find Surface Area

Example Question #26 : How To Find Surface Area

Example Question #27 : How To Find Surface Area

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