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:

$V=length\times width\times height$

So:

$V=6\times8\times13=624cm^3$

• The volume of a cone is given by:

$V=\frac{1}{3}\pi\times r^2\times\sqrt{s^2-r^2}$

So:

$V=\frac{1}{3}\times\pi\times4^2\times\sqrt{8^2-4^2}=116.1cm^3$

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).