Question

Two similar pyramids A and B have surface areas of 135cm^2 and 60cm^2 respectively . The volume of pyramid A is 405 cm^3 work out the volume of pyramid B

Answer 1

120cm³

Explanation:

√135/√60=3/2

3/2=1.5

1.5³=3.375

405/3.375=120

120cm³

Answer 2

120 cm^3

Explanation:

The surface areas are in the ratio 60 to 135 so the single dimensions are in the ratio √60 to √135.

Therefore the volumes are in the ratio (√60)^3 to (√135)^3 or 60^3/2 to 135^3/2.

So Volume of Pyramid B / Volume of Pyramid A

= 60^3/2 / 135^3/2.

Therefore we have the equation 60^3/2 / 135^3/2 = V / 405 where V is the volume of pyramid B.

V = (60^3/2 * 405) / 135^3/2

= 120 cm^3