Question

compare and contrast the formulas for the volume of a pyramid and the volume of a cone
because a pyramid has a non - circular base, the volume is always described in
square units, but the volume of a cone is stated in cubic units.
because a pyramid has a non - circular base, the volume is always described in
cubic units, but the volume of a cone is stated in square units.
both formulas are \\( \frac { 1 } { 3 } b h \\), but the base of a pyramid is always a square
both formulas are \\( \frac { 1 } { 3 } b h \\), but the base of a cone is always a circle

Explanation:

• Volume is always measured in cubic units, so options with square units (first two) are wrong.
• The formula for the volume of a pyramid is \(V=\frac{1}{3}Bh\) (where \(B\) is the area of the base and \(h\) is the height), and for a cone is \(V = \frac{1}{3}\pi r^{2}h=\frac{1}{3}Bh\) (since for a cone \(B=\pi r^{2}\), the area of the circular base). The base of a pyramid can be a triangle, rectangle, etc., not just a square. The base of a cone is always a circle.

Answer:

D. Both formulas are \(\frac{1}{3}Bh\), but the base of a cone is always a circle.