Question

a rectangular pyramid has a volume of 190 cubic centimeters. Find two possible sets of measurements for the base area and height of the pyramid

Answer 1

One possible set for the base area and height of the pyramid is 570 cm and 1 cm respectively

Other possible set for the base area and height of the pyramid is 285 cm and 2 cm respectively

Solution:

The volume of rectangular pyramid is given as:

`Volume = (1)/(3) * base\ area * height`

Given that,

Rectangular pyramid has a volume of 190 cubic centimeters

`190= (1)/(3) * base\ area * height`

Substitute, base area = 570 and height = 1

Then we get,

`190 = (1)/(3) * 570 * 1\\\\190 = 190`

Thus one possible set for the base area and height of the pyramid is 570 cm and 1 cm respectively

Substitute, base area = 285 and height = 2

`190 = (1)/(3) * 285 * 2\\\\190 = (1)/(3) * 570\\\\190 = 190`

Thus other possible set for the base area and height of the pyramid is 285 cm and 2 cm respectively