Non-Cubic Prisms - Math

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Question

The length of a box is 3 times the width. Which of the following gives the length (L inches) in terms of the width (W inches) of the box?

Answer

When reading word problems, there are certain clues that help interpret what is going on. The word “is” generally means “=” and the word “times” means it will be multiplied by something. Therefore, “the length of a box is 3 times the width” gives you the answer: L = 3 x W, or L = 3W.

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Question

The width of a box, in inches, is 5 inches less than three times its length. Which of the following equations gives the width, W inches, in terms of the length, L inches, of the box?

Answer

We notice the width is “5 inches less than three times its width,” so we express W as being three times its width (3L) and 5 inches less than that is 3L minus 5. In this case, W is the dependent and L is the independent variable.

W = 3L - 5

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Question

The length of a box is 3 times the width. Which of the following gives the length (L inches) in terms of the width (W inches) of the box?

Answer

When reading word problems, there are certain clues that help interpret what is going on. The word “is” generally means “=” and the word “times” means it will be multiplied by something. Therefore, “the length of a box is 3 times the width” gives you the answer: L = 3 x W, or L = 3W.

Compare your answer with the correct one above

Question

The width of a box, in inches, is 5 inches less than three times its length. Which of the following equations gives the width, W inches, in terms of the length, L inches, of the box?

Answer

We notice the width is “5 inches less than three times its width,” so we express W as being three times its width (3L) and 5 inches less than that is 3L minus 5. In this case, W is the dependent and L is the independent variable.

W = 3L - 5

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Question

What is the volume?

Answer

The volume is calculated using the equation:

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Question

A rectangular box has two sides with the following lengths:

and

If it possesses a volume of $84$ cm$^{3}$ , what is the area of its largest side?

Answer

The volume of a rectangular prism is found using the following formula:

$V=l\times w\times h$

If we substitute our known values, then we can solve for the missing side.

$84=3\times 4\times x$

Divide both sides of the equation by 12.

$\frac{84}{12}=\frac{12x}{12}$

We now know that the missing length equals 7 centimeters.

This means that the box can have sides with the following dimensions: 3cm by 4cm; 7cm by 3cm; or 7cm by 4cm. The greatest area of one side belongs to the one that is 7cm by 4cm.

$A=l\times w$

$A=4\times 7$

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Question

Find the volume of the following triangular prism.

Answer

The formula for the volume of a triangular prism is:

$V = \frac{1}{2} (l)(w)(h)$

Where is the length of the triangle, is the width of the triangle, and is the height of the prism

Plugging in our values, we get:

$V = \frac{1}{2} (6m)(6m)(9m)$

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Question

Find the volume of the following triangular prism.

Answer

The formula for the volume of a triangular prism is:

$V = \frac{1}{2}(l)(w)(h)$

Where is the length of the base, is the width of the base, and is the height of the prism

Plugging in our values, we get:

$V = \frac{1}{2}(8m)(8m)(12m)$

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Question

Find the volume of the following triangular prism:

Answer

The formula for the volume of an equilateral, triangular prism is:

$V = \left(\frac{s^2\sqrt{3}}{4}\right)(h)$

Where is the length of the triangle side and is the length of the height.

Plugging in our values, we get:

$V = \left(\frac{(6m)^2\sqrt{3}}{4}\right)(12m)$

$V=108\sqrt{3}m^3$

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Question

A rectangular box has two sides with the following lengths:

and

If it possesses a volume of $84$ cm$^{3}$ , what is the area of its largest side?

Answer

The volume of a rectangular prism is found using the following formula:

$V=l\times w\times h$

If we substitute our known values, then we can solve for the missing side.

$84=3\times 4\times x$

Divide both sides of the equation by 12.

$\frac{84}{12}=\frac{12x}{12}$

We now know that the missing length equals 7 centimeters.

This means that the box can have sides with the following dimensions: 3cm by 4cm; 7cm by 3cm; or 7cm by 4cm. The greatest area of one side belongs to the one that is 7cm by 4cm.

$A=l\times w$

$A=4\times 7$

Compare your answer with the correct one above

Question

Find the volume of the following triangular prism.

Answer

The formula for the volume of a triangular prism is:

$V = \frac{1}{2} (l)(w)(h)$

Where is the length of the triangle, is the width of the triangle, and is the height of the prism

Plugging in our values, we get:

$V = \frac{1}{2} (6m)(6m)(9m)$

Compare your answer with the correct one above

Question

Find the volume of the following triangular prism.

Answer

The formula for the volume of a triangular prism is:

$V = \frac{1}{2}(l)(w)(h)$

Where is the length of the base, is the width of the base, and is the height of the prism

Plugging in our values, we get:

$V = \frac{1}{2}(8m)(8m)(12m)$

Compare your answer with the correct one above

Question

Find the volume of the following triangular prism:

Answer

The formula for the volume of an equilateral, triangular prism is:

$V = \left(\frac{s^2\sqrt{3}}{4}\right)(h)$

Where is the length of the triangle side and is the length of the height.

Plugging in our values, we get:

$V = \left(\frac{(6m)^2\sqrt{3}}{4}\right)(12m)$

$V=108\sqrt{3}m^3$

Compare your answer with the correct one above

Question

What is the volume?

Answer

The volume is calculated using the equation:

Compare your answer with the correct one above

Question

The length of a box is 3 times the width. Which of the following gives the length (L inches) in terms of the width (W inches) of the box?

Answer

When reading word problems, there are certain clues that help interpret what is going on. The word “is” generally means “=” and the word “times” means it will be multiplied by something. Therefore, “the length of a box is 3 times the width” gives you the answer: L = 3 x W, or L = 3W.

Compare your answer with the correct one above

Question

The width of a box, in inches, is 5 inches less than three times its length. Which of the following equations gives the width, W inches, in terms of the length, L inches, of the box?

Answer

We notice the width is “5 inches less than three times its width,” so we express W as being three times its width (3L) and 5 inches less than that is 3L minus 5. In this case, W is the dependent and L is the independent variable.

W = 3L - 5

Compare your answer with the correct one above

Question

A rectangular box has two sides with the following lengths:

and

If it possesses a volume of $84$ cm$^{3}$ , what is the area of its largest side?

Answer

The volume of a rectangular prism is found using the following formula:

$V=l\times w\times h$

If we substitute our known values, then we can solve for the missing side.

$84=3\times 4\times x$

Divide both sides of the equation by 12.

$\frac{84}{12}=\frac{12x}{12}$

We now know that the missing length equals 7 centimeters.

This means that the box can have sides with the following dimensions: 3cm by 4cm; 7cm by 3cm; or 7cm by 4cm. The greatest area of one side belongs to the one that is 7cm by 4cm.

$A=l\times w$

$A=4\times 7$

Compare your answer with the correct one above

Question

Find the volume of the following triangular prism.

Answer

The formula for the volume of a triangular prism is:

$V = \frac{1}{2} (l)(w)(h)$

Where is the length of the triangle, is the width of the triangle, and is the height of the prism

Plugging in our values, we get:

$V = \frac{1}{2} (6m)(6m)(9m)$

Compare your answer with the correct one above

Question

Find the volume of the following triangular prism.

Answer

The formula for the volume of a triangular prism is:

$V = \frac{1}{2}(l)(w)(h)$

Where is the length of the base, is the width of the base, and is the height of the prism

Plugging in our values, we get:

$V = \frac{1}{2}(8m)(8m)(12m)$

Compare your answer with the correct one above

Question

Find the volume of the following triangular prism:

Answer

The formula for the volume of an equilateral, triangular prism is:

$V = \left(\frac{s^2\sqrt{3}}{4}\right)(h)$

Where is the length of the triangle side and is the length of the height.

Plugging in our values, we get:

$V = \left(\frac{(6m)^2\sqrt{3}}{4}\right)(12m)$

$V=108\sqrt{3}m^3$

Compare your answer with the correct one above

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