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HSPT Math : Concepts

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Example Questions

Example Question #1994 : Hspt Mathematics

$\textup{What is the volume of a sphere with a diameter of 14?}$

Possible Answers:

$196\pi$

$49\pi$

$\frac{49}{3}\pi$

$\frac{1372}{3} \pi$

$\frac{10976}{3} \pi$

Correct answer:

$\frac{1372}{3} \pi$

Explanation:

Write the formula for the volume of a sphere.

$V=\frac{4}{3}\pi r^3$

Since the diameter is 14 the radius is half the diameter, which is 7. Substitute the radius and solve for the volume.

$V=\frac{4}{3}\pi (7)^3= \frac{1372}{3} \pi$

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Example Question #1401 : Concepts

Find the area of a cylinder with radius 7 and height 2.

Possible Answers:

$49\pi$

$14\pi$

$28\pi$

$98\pi$

Correct answer:

$98\pi$

Explanation:

To solve, simply use the formula for the volume of a cylinder.

Thus,

$V=\pi{r^2}h$

Given the height is 2 and the radius is 7, substitute these values into the above formula to solve for volume.

$\\V=\pi*7^2*2\\V=\pi*49*2\\V=98\pi$

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Example Question #1403 : Concepts

Cylinder

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

Possible Answers:

$4,800 \pi$

$2,500 \pi$

$400 \pi$

$30,000 \pi$

Correct answer:

$4,800 \pi$

Explanation:

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

$V = \pi r^{2}h$

$V = \pi \cdot 20 ^{2} \cdot 30$

$V = \pi \cdot 400 \cdot 30$

$V =12,000 \pi$

40% of this volume is

$12,000 \pi \cdot \frac{40}{100} = 4,800 \pi$

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Example Question #214 : Geometry

Cylinder

The volume of the above cylinder is 80% of what number?

Possible Answers:

$2,625 \pi$

$45,000 \pi$

$1,680 \pi$

$28,000 \pi$

Correct answer:

$45,000 \pi$

Explanation:

The volume of the cylinder can be calculated by setting r = 30 and h = 40 in the formula

$V = \pi r^{2}h$

$V = \pi \cdot 30 ^{2} \cdot 40$

$V = \pi \cdot 900 \cdot 40$

$V =36,000 \pi$

This is 80% of the number

$36,000 \pi \div \frac{80}{100} = 36,000 \pi \cdot \frac{100} {80}= 45,000 \pi$

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Example Question #1402 : Concepts

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

Possible Answers:

$1,728 \pi$

$216 \pi$

$108 \pi$

$432 \pi$

Correct answer:

$216 \pi$

Explanation:

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

$V = \frac{4}{3} \pi r ^{3}$

$V = \frac{4}{3} \pi \cdot 6 ^{3} = \frac{4}{3} \pi \cdot 216 = 288 \pi$

75% of this is

$288 \pi \cdot \frac{75}{100} = 216 \pi$

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Example Question #1403 : Concepts

Find the volume of a rectangular prism with the following information:

$\\height=5 \\length=4 \\width=3$

Possible Answers:

$\frac{20}{3}$

Correct answer:

Explanation:

The formula for volume of a rectangular prism is,

V=length*width*height .

For this problem, since

$\\height=5 \\length=4 \\width=3$

the solution would be

V=5*4*3=60 .

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Example Question #1404 : Concepts

What is the measure of a right angle?

Possible Answers:

180

360

Correct answer:

Explanation:

The measure of a right angle is degrees.

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Example Question #1405 : Concepts

Triangle_a

Figure NOT drawn to scale.

If $w = 125^{\circ }$ and $x = 81^{\circ }$ , evaluate .

Possible Answers:

$44^{\circ }$

More information is needed to solve the problem.

$55^{\circ }$

$35^{\circ}$

$53^{\circ }$

Correct answer:

$44^{\circ }$

Explanation:

The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so

w = x + y

$y = w - x= 125 - 81 = 44^{\circ }$

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Example Question #106 : Properties Of Triangles

Triangle_a

Figure NOT drawn to scale.

If $x = 72^{\circ }$ and $y = 43^{\circ }$ , evaluate .

Possible Answers:

$65^{\circ}$

$137^{\circ}$

$108^{\circ}$

$115^{\circ }$

$125^{\circ }$

Correct answer:

$115^{\circ }$

Explanation:

The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so

$w = x + y = 72 + 43 = 115 ^{\circ }$

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Example Question #107 : Properties Of Triangles

If the vertex angle of an isoceles triangle is $64^{\circ}$ , what is the value of one of its base angles?

Possible Answers:

$36^{\circ}$

$116^{\circ}$

$58^{\circ}$

$64^{\circ}$

$26^{\circ}$

Correct answer:

$58^{\circ}$

Explanation:

In an isosceles triangle, the base angles are the same. Also, the three angles of a triangle add up to $180^{\circ}$ .

So, subtract the vertex angle from $180^{\circ}$ . You get $116^{\circ}$ .

Because there are two base angles you divide $116^{\circ}$ by , and you get $58^{\circ}$ .

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1994 : Hspt Mathematics

Example Question #1401 : Concepts

Example Question #1403 : Concepts

Example Question #214 : Geometry

Example Question #1402 : Concepts

Example Question #1403 : Concepts

Example Question #1404 : Concepts

Example Question #1405 : Concepts

Example Question #106 : Properties Of Triangles

Example Question #107 : Properties Of Triangles

All HSPT Math Resources

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