Question

Amanda says that a rectangular prism that is 6 cm long, 8 cm wide has a larger volume than a cone with a radius of 4 cm and a slant height of 8cm. Diego disagrees. explain who you think is correct and why.

Answer 1

Given the following information:

Rectangular Prism:

length = 6 cm

width = 8 cm

height = 13 cm

Cone:

slant height = 8 cm

r = 4 cm

Hence:

• The volume of a rectangular prism is given by:

`V=length* width* height`

So:

`V=6*8*13=624cm^3`

• The volume of a cone is given by:

`V=(1)/(3)\pi* r^2*√(s^2-r^2)`

So:

`V=(1)/(3)*\pi*4^2*√(8^2-4^2)=116.1cm^3`

ANSWER

Amanda was right because the volume of the prism is larger (624 cubic centimeters), compared with the volume of the cone (116.1 cubic centimeters).