How to find the length of an edge of a prism - Geometry

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Question

The height of a retangular prism is three times its width; its length is twice its width. Its surface area is 1,078 square inches. Give the width of the box.

Answer

Since the length of the box is twice the width and the height is three times the width, and .

The surface area of the box is

$A=4 W^{2}+12W^{2}+6W^{2}$

$A=22W^{2}$

To find the width:

$1,078=22W^{2}$

$W^{2} = 49$

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Question

Find the missing edge of the prism when its volume is .

Answer

The goal is to find the height of the rectangular prism with the given information of its width and length. The volume of a rectangular prism is $V = w \cdot l \cdot h$ , where is width and is height.

Because we're given the final volume and two of the three variables, we can substitute in the information we know and solve for the missing variable.

$600= 10 \cdot 12 \cdot h$

$600= 120 \cdot h$

$\frac{600}{120}=h$

Therefore, the height of the prism is .

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Question

The volume of a prism is .

Given the length is and the height is , find the width of the prism.

Answer

The volume of a prism is length times width times height.

We are given the length is 7m and the width is 5m.

So, we plug these into our formula:

$7\cdot5\cdot height=210$ .

We then solve for height:

$height=\frac{210}{7\cdot5}=\frac{210}{35}=6$ .

The height is therefore 6m.

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Question

A rectangular prism has a volume of cubic meters. Its length is twice its width, and its height is twice its length. What is the length of the prism?

Answer

If we let $\small w$ be the width of our prism, then since the length is twice the width, our length would be $\small 2w$ . Since the height is twice the length, our height would be $\small 4w$ .

Since the volume of a rectangular prism is simply the product of width, length, and height, we get

$\small V=lwh=w(2w)(4w)=8w^3=216$

We then simply solve for the width.

$\small 8w^3=216$

$\small w^3=27$

$\small w=3$

Therefore, our width is 3. Since our length is twice the width, the length is 6.

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Question

A right, rectangular prism has a volume of cubic inches. Its width is inches and its height is inches. What is its length?

Answer

The formula for the volume of a right, rectangular prism is , so substitute the known values and solve for lenght.

$240 = l(5)(6) \rightarrow 240 = 30l \rightarrow8 = l$ . So the length is 8 inches.

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Question

The surface area of a right rectangular prism is square cm. Its length is cm and its height is cm. Find the width of the prism.

Answer

Use the formula for finding the surface area of a right, rectangular prism,

and substitute the known values, and then solve for w.

So,

$358 = 2(12)(w) + 2(w)(5) + 2(12)(5) \rightarrow 358 = 24w + 10w + 120$

$\rightarrow 238 = 34w \rightarrow w = 7$

So, the width is 7 cm.

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Question

The height of a retangular prism is three times its width; its length is twice its width. Its surface area is 1,078 square inches. Give the width of the box.

Answer

Since the length of the box is twice the width and the height is three times the width, and .

The surface area of the box is

$A=4 W^{2}+12W^{2}+6W^{2}$

$A=22W^{2}$

To find the width:

$1,078=22W^{2}$

$W^{2} = 49$

Compare your answer with the correct one above

Question

Find the missing edge of the prism when its volume is .

Answer

The goal is to find the height of the rectangular prism with the given information of its width and length. The volume of a rectangular prism is $V = w \cdot l \cdot h$ , where is width and is height.

Because we're given the final volume and two of the three variables, we can substitute in the information we know and solve for the missing variable.

$600= 10 \cdot 12 \cdot h$

$600= 120 \cdot h$

$\frac{600}{120}=h$

Therefore, the height of the prism is .

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Question

The volume of a prism is .

Given the length is and the height is , find the width of the prism.

Answer

The volume of a prism is length times width times height.

We are given the length is 7m and the width is 5m.

So, we plug these into our formula:

$7\cdot5\cdot height=210$ .

We then solve for height:

$height=\frac{210}{7\cdot5}=\frac{210}{35}=6$ .

The height is therefore 6m.

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Question

A rectangular prism has a volume of cubic meters. Its length is twice its width, and its height is twice its length. What is the length of the prism?

Answer

If we let $\small w$ be the width of our prism, then since the length is twice the width, our length would be $\small 2w$ . Since the height is twice the length, our height would be $\small 4w$ .

Since the volume of a rectangular prism is simply the product of width, length, and height, we get

$\small V=lwh=w(2w)(4w)=8w^3=216$

We then simply solve for the width.

$\small 8w^3=216$

$\small w^3=27$

$\small w=3$

Therefore, our width is 3. Since our length is twice the width, the length is 6.

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Question

A right, rectangular prism has a volume of cubic inches. Its width is inches and its height is inches. What is its length?

Answer

The formula for the volume of a right, rectangular prism is , so substitute the known values and solve for lenght.

$240 = l(5)(6) \rightarrow 240 = 30l \rightarrow8 = l$ . So the length is 8 inches.

Compare your answer with the correct one above

Question

The surface area of a right rectangular prism is square cm. Its length is cm and its height is cm. Find the width of the prism.

Answer

Use the formula for finding the surface area of a right, rectangular prism,

and substitute the known values, and then solve for w.

So,

$358 = 2(12)(w) + 2(w)(5) + 2(12)(5) \rightarrow 358 = 24w + 10w + 120$

$\rightarrow 238 = 34w \rightarrow w = 7$

So, the width is 7 cm.

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Question

The height of a retangular prism is three times its width; its length is twice its width. Its surface area is 1,078 square inches. Give the width of the box.

Answer

Since the length of the box is twice the width and the height is three times the width, and .

The surface area of the box is

$A=4 W^{2}+12W^{2}+6W^{2}$

$A=22W^{2}$

To find the width:

$1,078=22W^{2}$

$W^{2} = 49$

Compare your answer with the correct one above

Question

Find the missing edge of the prism when its volume is .

Answer

The goal is to find the height of the rectangular prism with the given information of its width and length. The volume of a rectangular prism is $V = w \cdot l \cdot h$ , where is width and is height.

Because we're given the final volume and two of the three variables, we can substitute in the information we know and solve for the missing variable.

$600= 10 \cdot 12 \cdot h$

$600= 120 \cdot h$

$\frac{600}{120}=h$

Therefore, the height of the prism is .

Compare your answer with the correct one above

Question

The volume of a prism is .

Given the length is and the height is , find the width of the prism.

Answer

The volume of a prism is length times width times height.

We are given the length is 7m and the width is 5m.

So, we plug these into our formula:

$7\cdot5\cdot height=210$ .

We then solve for height:

$height=\frac{210}{7\cdot5}=\frac{210}{35}=6$ .

The height is therefore 6m.

Compare your answer with the correct one above

Question

A rectangular prism has a volume of cubic meters. Its length is twice its width, and its height is twice its length. What is the length of the prism?

Answer

If we let $\small w$ be the width of our prism, then since the length is twice the width, our length would be $\small 2w$ . Since the height is twice the length, our height would be $\small 4w$ .

Since the volume of a rectangular prism is simply the product of width, length, and height, we get

$\small V=lwh=w(2w)(4w)=8w^3=216$

We then simply solve for the width.

$\small 8w^3=216$

$\small w^3=27$

$\small w=3$

Therefore, our width is 3. Since our length is twice the width, the length is 6.

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Question

A right, rectangular prism has a volume of cubic inches. Its width is inches and its height is inches. What is its length?

Answer

The formula for the volume of a right, rectangular prism is , so substitute the known values and solve for lenght.

$240 = l(5)(6) \rightarrow 240 = 30l \rightarrow8 = l$ . So the length is 8 inches.

Compare your answer with the correct one above

Question

The surface area of a right rectangular prism is square cm. Its length is cm and its height is cm. Find the width of the prism.

Answer

Use the formula for finding the surface area of a right, rectangular prism,

and substitute the known values, and then solve for w.

So,

$358 = 2(12)(w) + 2(w)(5) + 2(12)(5) \rightarrow 358 = 24w + 10w + 120$

$\rightarrow 238 = 34w \rightarrow w = 7$

So, the width is 7 cm.

Compare your answer with the correct one above

Question

The height of a retangular prism is three times its width; its length is twice its width. Its surface area is 1,078 square inches. Give the width of the box.

Answer

Since the length of the box is twice the width and the height is three times the width, and .

The surface area of the box is

$A=4 W^{2}+12W^{2}+6W^{2}$

$A=22W^{2}$

To find the width:

$1,078=22W^{2}$

$W^{2} = 49$

Compare your answer with the correct one above

Question

Find the missing edge of the prism when its volume is .

Answer

The goal is to find the height of the rectangular prism with the given information of its width and length. The volume of a rectangular prism is $V = w \cdot l \cdot h$ , where is width and is height.

Because we're given the final volume and two of the three variables, we can substitute in the information we know and solve for the missing variable.

$600= 10 \cdot 12 \cdot h$

$600= 120 \cdot h$

$\frac{600}{120}=h$

Therefore, the height of the prism is .

Compare your answer with the correct one above

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