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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 #3 : How To Find The Volume Of A Rectangular Solid In Pre Algebra

What is the side of a cube if its volume is 125 ?

Possible Answers:

Correct answer:

Explanation:

The formula for volume of a cube is V=s*s*s or V=s^3 .

For this cube that means 125=s^3 .

Take the cube root of both sides:

$\sqrt[3]{125}=\sqrt[3]{s^3}$

5=s

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

What is the volume of a rectangular prism with a length of , height of , and width of ?

Possible Answers:

216

Correct answer:

Explanation:

The formula for volume of a rectangular prism is V=l*w*h .

Plug in our given information:

V=6*3*4

V=72

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

What is the volume of a rectangular prism with a length of , width of , and height of ?

Possible Answers:

210

Correct answer:

210

Explanation:

The formula for volume of a rectangular prism is V=l*w*h .

Plug in our given information:

V=7*5*6

V=210

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

What is the volume of a cube with a side length of ?

Possible Answers:

V=256

V=4096

V=16

V=64

Correct answer:

V=4096

Explanation:

To find the volume of a cube you must cube the side length.

The equation looks like this: $Volume=s^{3}$

Cube the side length, , to find the answer: $V=16^{3}$

The answer is V=4096 .

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

What is the volume of a rectangular solid with a base of , length of , and height of ?

Possible Answers:

V=756

V=28

V=326

Correct answer:

V=756

Explanation:

To find the volume of a rectangular solid we must know the equation: Volume=b*l*h

We then plug in our numbers for base, length, and height: Volume=7*9*12

Multiply to get the answer of V=756 .

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

What is the volume of a cube with a side length of ?

Possible Answers:

V=16

V=32

V=64

V=128

Correct answer:

V=64

Explanation:

To find the volume of a cube you must find the cube root of the side length.

The equation looks like this

$V=s^{3}$

Cube the side length, to find the answer

$V=4^{3}$

The answer is V=64 .

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Example Question #6 : How To Find The Volume Of A Rectangular Solid In Pre Algebra

What is the volume of a rectangular solid with a base of , length of , and a height of ?

Possible Answers:

V=40

V=400

V=360

V=270

Correct answer:

V=360

Explanation:

To find the volume of a rectangular solid we must know the equation is

V=Base*Height*Length

We then plug in our numbers for base, length, and height

$V=8\cdot 5\cdot 9$

Multiply to get the answer of V=360 .

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Example Question #1 : 45/45/90 Right Isosceles Triangles

Isosceles

In an isosceles right triangle, two sides equal . Find the length of side .

Possible Answers:

$\sqrt{x}$

$2\sqrt{2}$

$x\sqrt{2}$

$\sqrt{2}$

Correct answer:

$x\sqrt{2}$

Explanation:

This problem represents the definition of the side lengths of an isosceles right triangle. By definition the sides equal , , and $x\sqrt{2}$ . However, if you did not remember this definition one can also find the length of the side using the Pythagorean theorem $(a^{2}+b^{2}=c^{2})$ .

$h^{2}=x^{2}+x^{2}$

$h^{2}=2x^{2}$

$h=\sqrt{2x^{2}}$

$\rightarrow x\sqrt{2}$

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Example Question #1 : 45/45/90 Right Isosceles Triangles

ABCD is a square whose side is units. Find the length of diagonal AC.

Possible Answers:

$8\sqrt{3}$

none of the other answers

$8 \sqrt{2}$

Correct answer:

$8 \sqrt{2}$

Explanation:

To find the length of the diagonal, given two sides of the square, we can create two equal triangles from the square. The diagonal line splits the right angles of the square in half, creating two triangles with the angles of , , and degrees. This type of triangle is a special right triangle, with the relationship between the side opposite the degree angles serving as x, and the side opposite the degree angle serving as $x\sqrt{2}$ .

Appyling this, if we plug in for we get that the side opposite the right angle (aka the diagonal) is $8\sqrt{2}$

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Example Question #1 : 45/45/90 Right Isosceles Triangles

The area of a square is 144 . Find the length of the diagonal of the square.

Possible Answers:

$4\sqrt{2}$

$16\sqrt{2}$

$12\sqrt{2}$

Correct answer:

$12\sqrt{2}$

Explanation:

If the area of the square is 144 , we know that each side of the square is , because the area of a square is $s^{2}$ .

Then, the diagonal creates two 45/45/90 special right triangles. Knowing that the sides = , we can find that the hypotenuse (aka diagonal) is $12\sqrt{2}$

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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 #3 : How To Find The Volume Of A Rectangular Solid In Pre Algebra

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

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

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

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

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

Example Question #6 : How To Find The Volume Of A Rectangular Solid In Pre Algebra

Example Question #1 : 45/45/90 Right Isosceles Triangles

Example Question #1 : 45/45/90 Right Isosceles Triangles

Example Question #1 : 45/45/90 Right Isosceles Triangles

All High School Math Resources

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