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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #821 : High School Math

What is the volume of a pyramid with a base length of 5 inches, base width of 6 inches, and height of 8 inches?

Possible Answers:

$60\ in^3$

$80\ in^3$

$120\ in^3$

$240\ in^3$

Correct answer:

$80\ in^3$

Explanation:

The volume of a pyramid can be determined using the equation:

$V=\frac{1}{3}lwh=\frac{1}{3}(5\ in)(6\ in)(8\ in)=\frac{1}{3}240\ in^3=80\ in^3$

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Example Question #1 : How To Find The Volume Of A Pyramid In Pre Algebra

What is the volume of a square-based pyramid with side lengths and a height of ?

Possible Answers:

300

734

448

1334

Correct answer:

448

Explanation:

To find the volume of a pyramid, use the equation:

$Volume=\frac{1}{3}(Base\ Area)(Height)$

First solve for the base area (which is a square) using $Base\ Area=Side^{2}$

$Base\ Area=8^{2}$

$Base\ Area=64$

Then subsitute the base area into the volume formula and obtain:

$Volume=(\frac{1}{3})(64)(21)$

Volume=448

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Example Question #822 : High School Math

What is the volume of a cone with a base radius of and a height of ?

Possible Answers:

100

$60\pi$

$100\pi$

Correct answer:

$100\pi$

Explanation:

To find the volume of a cone we must use the equation

$Volume\ of\ \ cone=\frac{1}{3}\cdot (area\ of\ base)\cdot (height)$

We must first solve for the area of the base using .

The equation for the area of a circle is

We plug in and square it to get

We then plug our answer into the equation for the cone with to get

We multiply to get our final answer for the volume of the cone .

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Example Question #1 : How To Find The Volume Of A Cone In Pre Algebra

What is the volume of a cone with a circle radius of and a height of ?

Possible Answers:

$448\pi$

$360\pi$

168

$168\pi$

Correct answer:

$448\pi$

Explanation:

To find the volume of a cone we must use the equation

We must first solve for the area of the circle using r=8

The equation for the area of a circle is

We plug in and square it to get

$Area=\pi(64)$

We then plug our answer into the equation for the cone with h=21 to get

$Volume=(\frac{1}{3})(64\pi)(21)$

We multiply to get our final answer for the volume of the cone $448\pi$ .

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Example Question #822 : High School Math

What is the volume of a cone with a circle radius of and a height of ?

Possible Answers:

$1152\pi$

$384\pi$

384

1152

Correct answer:

$384\pi$

Explanation:

To find the volume of a cone we must use the equation

We must first solve for the area of the circle using r=8

The equation for the area of a circle is

We plug in and square it to get $Area=64\pi$

We then plug our answer into the equation for the cone with h=18 to get

$V=(\frac{1}{3})(64\pi)(18)$

We multiply to get our final answer for the volume of the cone $384\pi$ .

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Example Question #4 : How To Find The Volume Of A Cone In Pre Algebra

What is the volume of a cone with a radius of and a height of ?

Possible Answers:

$60\pi$

$30\pi$

$100\pi$

$150\pi$

Correct answer:

$150\pi$

Explanation:

To find the volume of a cone, use the equation:

$Volume=\frac{1}{3}(Area\ of\ Circle)(Height)$

Solve for the area of a circle with radius :

$Area\ of\ Circle=\pi(5^{2})$

$Area\ of\ Circle = 25\pi$

Substitute $25\pi$ for area of circle and for height into the equation for volume

$Volume=\frac{1}{2}(25\pi)(12)$

$Volume=150\pi$ .

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Example Question #823 : High School Math

What is the volume of a cone with a height of meters and a base diameter of meters?

Possible Answers:

$36\pi \ m^3$

$54\pi \ m^3$

$9\pi \ m^3$

$18\pi \ m^3$

$72\pi \ m^3$

Correct answer:

$18\pi \ m^3$

Explanation:

The formula for the volume of a cone is $\frac{1}{3}{\pi}r^{2}h$ .

Notice that we are given the diameter, meters, not the radius; thus, we have to solve for the radius by dividing the diameter by two. The radius is therefore 3 meters. Then, we plug this value into the formula for volume:

$\frac{1}{3}{\pi}(3)^{2}\cdot 6 = \frac{1}{3}{\pi}9\cdot 6 = 18{\pi}\ \textup{meters}^3=18\pi m^3$

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Example Question #1 : How To Find The Volume Of A Sphere In Pre Algebra

What is the volume of a sphere with a radius of ?

Possible Answers:

$49\pi$

$571.55\pi$

$343\pi$

$457.33\pi$

Correct answer:

$457.33\pi$

Explanation:

To solve for the volume of a sphere you must first know the equation for the volume of a sphere.

The equation is

Then plug the radius into the equation for yielding $V=\frac{4}{3}\pi(7^{3})$

Then cube the radius to get $V=\frac{4}{3}\pi(343)$

Multiply the answer by $\frac{4}{3}$ and to yield $457.33\pi$ .

The answer is $457.33\pi$ .

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Example Question #2 : How To Find The Volume Of A Sphere In Pre Algebra

What is the volume of a sphere with a radius of ?

Possible Answers:

$9\pi$

$81\pi$

$27\pi$

$36\pi$

$\frac{4}{3}\pi$

Correct answer:

$36\pi$

Explanation:

The formula for the volume of a sphere is $V=\frac{4}{3}\pi r^3$ .

Plug in our radius to solve:

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

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

$V=\frac{4}{3}*\pi*27$

$V=36\pi$

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Example Question #3 : How To Find The Volume Of A Sphere In Pre Algebra

What is the volume of a sphere with a radius of ?

Possible Answers:

$216\pi$

$96\pi$

$288\pi$

$48\pi$

$36\pi$

Correct answer:

$288\pi$

Explanation:

The formula for the volume of a sphere is $V=\frac{4}{3}\pi r^3$ .

Plug in our radius to solve:

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

$V=\frac{4}{3}\pi *6^3$

$V=\frac{4}{3}*\pi*216$

$V=288\pi$

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #821 : High School Math

Example Question #1 : How To Find The Volume Of A Pyramid In Pre Algebra

Example Question #822 : High School Math

Example Question #1 : How To Find The Volume Of A Cone In Pre Algebra

Example Question #822 : High School Math

Example Question #4 : How To Find The Volume Of A Cone In Pre Algebra

Example Question #823 : High School Math

Example Question #1 : How To Find The Volume Of A Sphere In Pre Algebra

Example Question #2 : How To Find The Volume Of A Sphere In Pre Algebra

Example Question #3 : How To Find The Volume Of A Sphere In Pre Algebra

All High School Math Resources

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