Question

Mr. Murphy is designing a rectangular concrete fire pit. The concrete sides and bottom will be 5 inches thick. The interior length will be 3 times the interior height, and the interior width will be 2 times the interior height. What should the outer dimensions of the fire pit be if the inner volume is to be 6000 cubic inches

Answer 1

To find the outer dimensions of the fire pit, you can calculate the inner dimensions based on the given information. Then, add the thickness of the concrete to the inner dimensions to get the outer dimensions. The outer dimensions of the fire pit should be 35 inches in length, 30 inches in width, and 25 inches in height.

Step-by-step explanation:

To find the outer dimensions of the fire pit, we can start by calculating the inner dimensions based on the given information. Let's assume the interior height of the fire pit is h inches. According to the problem, the interior length is 3 times the interior height, so it would be 3h inches. Similarly, the interior width is 2 times the interior height, so it would be 2h inches.

To find the volume of the fire pit, we can use the formula V = length x width x height. Substituting the values we found, the inner volume is 3h x 2h x h = 6h³ cubic inches.

Given that the inner volume is 6000 cubic inches, we can set up the equation 6h³ = 6000 and solve for h. Dividing both sides by 6, we get h³ = 1000. Taking the cube root of both sides, we find that h = 10.

Now, we can calculate the outer dimensions of the fire pit by adding the thickness of the concrete to the inner dimensions. The outer length would be 3h + 2(5) inches, the outer width would be 2h + 2(5) inches, and the outer height would be h + 2(5) inches.

Therefore, the outer dimensions of the fire pit should be 35 inches in length, 30 inches in width, and 25 inches in height.

Answer 2

For the outer dimensions: length = 35 inches, width = 25 inches, and height = 15 inches.

Step-by-step explanation:

For the interior;

volume = 6000
`in^(3)`

length, l = 3h

width, w = 2h

height = h

But,

Volume of a cuboid = length x width x height

So that;

6000 = 3h x 2h x h

6000 = 6
`h^(3)`

Divide through by 6 to have;

1000 =
`h^(3)`

h =
`\sqrt[3]{1000}`

= 10

Thus, the height is 10 inches. Thus;

length, l = 3h = 3 x 10 = 30 inches

width, w = 2h = 2 x 10 = 20 inches

For the outer dimension, since the concrete sides and bottom would be 5 inches thick. Then its dimension are;

length, l = 30 + 5 = 35 inches

width, w = 20 + 5 = 25 inches

height = 10 + 5 = 15 inches