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HSPT Math : How to find surface area

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Example Question #6 : How To Find The Surface Area Of A Sphere

The area of a circle with radius 4 divided by the surface area of a sphere with radius 2 is equal to:

Possible Answers:

0.5

Correct answer:

Explanation:

The surface area of a sphere is 4πr². The area of a circle is πr². 16/16 is equal to 1.

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Example Question #1 : How To Find The Surface Area Of A Sphere

What is the ratio of the surface area of a cube to the surface area of a sphere inscribed within it?

Possible Answers:

6/π

4/π

π/3

3/π

2π

Correct answer:

6/π

Explanation:

Let's call the radius of the sphere r. The formula for the surface area of a sphere (A) is given below:

A = 4πr²

Because the sphere is inscribed inside the cube, the diameter of the sphere is equal to the side length of the cube. Because the diameter is twice the length of the radius, the diameter of the sphere is 2r. This means that the side length of the cube is also 2r.

The surface area for a cube is given by the following formula, where s represents the length of each side of the cube:

surface area of cube = 6s²

The formula for surface area of a cube comes from the fact that each face of the cube has an area of s², and there are 6 faces total on a cube.

Since we already determined that the side length of the cube is the same as 2r, we can replace s with 2r.

surface area of cube = 6(2r)²= 6(2r)(2r) = 24r².

We are asked to find the ratio of the surface area of the cube to the surface area of the sphere. This means we must divide the surface area of the cube by the surface area of the sphere.

ratio = (24r²)/(4πr²)

The r²term cancels in the numerator and denominator. Also, 24/4 simplifes to 6.

ratio = (24r²)/(4πr²) = 6/π

The answer is 6/π.

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Example Question #8 : How To Find The Surface Area Of A Sphere

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

Possible Answers:

$16\pi \ cm^{2}$

$8\pi \ cm^{2}$

$12\pi \ cm^{2}$

$20\pi \ cm^{2}$

$18\pi \ cm^{2}$

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 #2112 : Hspt Mathematics

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

Possible Answers:

$14\pi$

$100\pi$

$10\pi$

$40\pi$

$400 \pi$

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 #2121 : Hspt Mathematics

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

Possible Answers:

600

760

100

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 #1523 : Concepts

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 #2122 : Hspt Mathematics

Find the surface area of a cube with side length .

Possible Answers:

8x^3

16x^2

4x^2

24x^2

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 #2123 : Hspt Mathematics

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

Possible Answers:

150

100

125

200

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 #342 : Geometry

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

Possible Answers:

$1,728 \pi$

$108 \pi$

$432 \pi$

$216 \pi$

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 #2121 : Hspt Mathematics

Cylinder

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

Possible Answers:

$800 \pi$

$2,500 \pi$

$30,000 \pi$

$4,800 \pi$

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 : How to find surface area

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #6 : How To Find The Surface Area Of A Sphere

Example Question #1 : How To Find The Surface Area Of A Sphere

Example Question #8 : How To Find The Surface Area Of A Sphere

Example Question #2112 : Hspt Mathematics

Example Question #2121 : Hspt Mathematics

Example Question #1523 : Concepts

Example Question #2122 : Hspt Mathematics

Example Question #2123 : Hspt Mathematics

Example Question #342 : Geometry

Example Question #2121 : Hspt Mathematics

All HSPT Math Resources

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