Question

A pyramid has a base with a demension 5 inches by 7 inches .The height of the pyramid is unknown .If the volume of the pyramid is 105 cubic inches,what is the height of the pyramid ?Explain the steps

Answer 1

Sample Response: Substitute the area of the base and the volume into the formula V = 1

3

Bh. After substituting, you have 105 = 1

3

(35)h. Solve for h by multiplying both sides by 3 and then dividing both sides by 35. The height is 9 inches.

Explanation:

Answer 2

9 inches

Explanation:

The volume of a pyramid is given as:

`V = (l* w*h)/(3)`

where l = length of base of pyramid

w = width of base of pyramid

h = height of pyramid

The volume of the cylinder is already known (
`105 in^3` ) and the other two dimensions are known as 5 in and 7 in.

From the formula of the volume of the pyramid, the height of the pyramid is given as:

`h = (3V)/(l*h)`

Hence, the height of the pyramid is:

`h = (3 * 105)/(5 * 7)\\ \\h = (315)/(35) = 9in`

The pyramid's height is 9 inches.