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

What is the volume of a sphere with a radius of $\pi$ ?

Possible Answers:

$\frac{\pi}{4}$

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

Undefined

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

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

Correct answer:

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

Explanation:

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

Plug in our radius to solve:

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

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

Remember, an exponent just means a number times itself. That means that $\pi*\pi^3=\pi^4$ .

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

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Example Question #5 : How To Find The Volume Of A Sphere In Pre Algebra

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

Possible Answers:

$8\pi$

$10\tfrac{2}{3}\pi$

$6\pi$

$21\tfrac{1}{3}\pi$

$64\pi$

Correct answer:

$10\tfrac{2}{3}\pi$

Explanation:

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

Plug in our radius to solve:

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

$V=\frac{4}{3}\pi *2^3$

$V=\frac{4}{3}*\pi*8$

$V=10\tfrac{2}{3}\pi$

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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:

$375\pi$

$84\tfrac{1}{3}\pi$

$500\pi$

$125\pi$

$166\tfrac{2}{3}\pi$

Correct answer:

$166\tfrac{2}{3}\pi$

Explanation:

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

Plug in our radius to solve:

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

$V=\frac{4}{3}\pi *5^3$

$V=\frac{4}{3}*\pi*125$

$V=166\tfrac{2}{3}\pi$

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Example Question #831 : High School Math

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

Possible Answers:

$108\pi$

$36\pi$

$27\pi$

$6\pi$

$12\pi$

Correct answer:

$36\pi$

Explanation:

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

Plug in our given values.

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

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

$V=36\pi$

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Example Question #8 : How To Find The Volume Of A Sphere In Pre Algebra

If the volume of a sphere is $300\pi$ , what is the radius?

Possible Answers:

6.08

1.94

$6.08\pi$

225

Correct answer:

6.08

Explanation:

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

Plug in our given information.

$300\pi=\frac{4}{3}\pi r^3$

Notice that the $\pi$ 's cancel out.

$300=\frac{4}{3}r^3$

Divide both sides by $\frac{4}{3}$ . Since we're dividing by a fraction, that means we need to multiply both sides by the reciprocal: $\frac{3}{4}$ .

$300*\frac{3}{4}=r^3$

225=r^3

$\sqrt[3]{225}=\sqrt[3]{r^3}$

$\sqrt[3]{225}=r$

6.08=r

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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:

$8000\pi$

$6453\pi$

$7776\pi$

$4800\pi$

Correct answer:

$7776\pi$

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

$V=(\frac{4}{3})(18^{3})(\pi)$

Then cube the radius to get

$V=(\frac{4}{3})(5832)(\pi)$

Multiply the answer by and to yield $V=7776\pi$ .

The answer is $7776\pi$ .

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Example Question #10 : How To Find The Volume Of A Sphere In Pre Algebra

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

Possible Answers:

$V=45\pi$

$V=27\pi$

$V=9\pi$

$V=36\pi$

Correct answer:

$V=36\pi$

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

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

Then cube the radius to get

$V=\frac{4}{3}(27})(\pi)$

Multiply the answer by and to yield

$V=36\pi$ .

The answer is $V=36\pi$ .

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Example Question #832 : High School Math

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

Possible Answers:

$972 \pi$

$729\pi$

$693\pi$

$1272\pi$

Correct answer:

$972 \pi$

Explanation:

To solve for the volume of a sphere, use the equation:

$Volume=\frac{4}{3}(\pi)(radius^{3})$

Substitute the given radius into the equation:

$Volume=\frac{4}{3}(\pi)(9^{3})$

$Volume=(\frac{4}{3})(\pi)(729)$

$Volume=972 \pi$

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Example Question #1 : Acute / Obtuse Triangles

Two similiar triangles have a ratio of perimeters of $7:2$ .

If the smaller triangle has sides of 3, 7, and 5, what is the perimeter of the larger triangle.

Possible Answers:

$49.5$

$50.5$

$51.5$

$52.5$

$48.5$

Correct answer:

$52.5$

Explanation:

Adding the sides gives a perimeter of 15 for the smaller triangle. Multipying by the given ratio of $\frac{7}{2}$ , yields 52.5.

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Example Question #131 : Triangles

Two sides of an isosceles triangle are 20 and 30. What is the difference of the largest and the smallest possible perimeters?

Possible Answers:

The answer cannot be determined

Correct answer:

Explanation:

The trick here is that we don't know which is the repeated side. Our possible triangles are therefore 20 + 20 + 30 = 70 or 30 + 30 + 20 = 80. The difference is therefore 80 – 70 or 10.

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

Example Question #5 : How To Find The Volume Of A Sphere In Pre Algebra

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

Example Question #831 : High School Math

Example Question #8 : 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

Example Question #10 : How To Find The Volume Of A Sphere In Pre Algebra

Example Question #832 : High School Math

Example Question #1 : Acute / Obtuse Triangles

Example Question #131 : Triangles

All High School Math Resources

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