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Intermediate Geometry : How to find the length of an edge of a prism

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Example Question #1 : How To Find The Length Of An Edge Of A Prism

The volume of a prism is 210m^3 .

Given the length is and the height is 5 m , find the width of the prism.

Possible Answers:

12 m

8 m

70 m

6 m

93 m

Correct answer:

6 m

Explanation:

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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Example Question #1 : How To Find The Length Of An Edge Of A Prism

Find the missing edge of the prism when its volume is $600 \:units^3$ .

Find_the_edge

Possible Answers:

$10\:units$

$2\sqrt{61}$

15.6

$5\:units$

Correct answer:

$5\:units$

Explanation:

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.

$600= 10 \cdot 12 \cdot h$

$600= 120 \cdot h$

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

h=5

Therefore, the height of the prism is $5\:units$ .

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Example Question #1 : How To Find The Length Of An Edge Of A Prism

A rectangular prism has a volume of 216 cubic meters. Its length is twice its width, and its height is twice its length. What is the length of the prism?

Possible Answers:

3 m

8 m

2 m

6 m

12 m

Correct answer:

6 m

Explanation:

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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Example Question #2 : How To Find The Length Of An Edge Of A Prism

A right, rectangular prism has a volume of 240 cubic inches. Its width is inches and its height is inches. What is its length?

Possible Answers:

210in

48in

8in

16in

None of the other answers.

Correct answer:

8in

Explanation:

The formula for the volume of a right, rectangular prism is V=lwh , 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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Example Question #1 : How To Find The Length Of An Edge Of A Prism

The surface area of a right rectangular prism is 358 square cm. Its length is cm and its height is cm. Find the width of the prism.

Possible Answers:

34.8cm

14.5cm

13.8cm

None of the other answers.

7cm

Correct answer:

7cm

Explanation:

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

SA = 2lw + 2wh + 2lh

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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Example Question #2 : How To Find The Length Of An Edge Of A Prism

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.

Possible Answers:

$14 \; \textrm{in}$

$21\; \textrm{in}$

$7 \; \textrm{in}$

$28 \; \textrm{in}$

$42 \; \textrm{in}$

Correct answer:

$7 \; \textrm{in}$

Explanation:

Since the length of the box is twice the width and the height is three times the width, L=2W and H=3W .

The surface area of the box is

A=2LW+2LH+2WH

A=2(2W) W+2(2W)(3W)+2W(3W)

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

$A=22W^{2}$

To find the width:

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

$W^{2} = 49$

W=7

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Intermediate Geometry : How to find the length of an edge of a prism

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find The Length Of An Edge Of A Prism

Example Question #1 : How To Find The Length Of An Edge Of A Prism

Example Question #1 : How To Find The Length Of An Edge Of A Prism

Example Question #2 : How To Find The Length Of An Edge Of A Prism

Example Question #1 : How To Find The Length Of An Edge Of A Prism

Example Question #2 : How To Find The Length Of An Edge Of A Prism

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