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:

$Volume = \frac{1}{3} \times base\ area \times height$

Given that,

Rectangular pyramid has a volume of 190 cubic centimeters

$190= \frac{1}{3} \times base\ area \times height$

Substitute, base area = 570 and height = 1

Then we get,

$190 = \frac{1}{3} \times 570 \times 1\\\\190 = 190$

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

$190 = \frac{1}{3} \times 285 \times 2\\\\190 = \frac{1}{3} \times 570\\\\190 = 190$

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