Cone W has a radius of 8 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W. Paul and Manuel disagree on how the volumes of cone W and square pyramid X are related. Examine their arguments. Which statement explains whose
argument is correct and why?
Paul
Manuel
The volume of square pyramid X is equal to the volume of cone W. This can
be proven by finding the base area and volume of cone W, along with the
volume of square pyramid X. The base area of cone Wis TI(14) = T(82) =
(200.96)(5)
1
200.96 cm2. The volume of cone Wis (area of base)(h) = 3
31/ care
The volume of square pyramid X is three times the volume of cone W. This
can be proven by finding the base area and volume of cone W, along with the
volume of square pyramid X. The base area of cone Wis 7(12) = T(82) =
=
3
334.93 cm. The volume of square pyramid X is (area of base)(h) = (200.96)
(5) = 1,004.8 cm?
(area of base)(h) =
334.93 cm. The volume of square pyramid X is
(200.96)(5) = 334.93 cm.
1
3