Question

A frustum is formed when a plane parallel to a cone’s base cuts off the upper portion as shown. A cone is shown. The top of the cone is cut off to form a frustum of the bottom portion. The cone has a radius of 3. 5 and a height of 8. The frustum has a height of 11 and a radius of 7. 5. Which expression represents the volume, in cubic units, of the frustum? One-thirdĎ€(7. 52)(11) â€" One-thirdĎ€(3. 52)(8) One-thirdĎ€(7. 52)(11) One-thirdĎ€(3. 52)(8) One-thirdĎ€(7. 52)(19) â€" One-thirdĎ€(3. 52)(8) One-thirdĎ€(7. 52)(19) One-thirdĎ€(3. 52)(8).

Answer 1

The expression that represents the volume of the frustum in cubic units is $\frac{1}{3} \pi (7.5)^2(19) - \frac{1}{3} \pi (3.5)^2(8)$$units^3$

The formula for calculating the volume of a cone is expressed as:

$V=\frac{1}{3} \pi r^2h$

• r is the base radius of the cone

• h is the height of the cone

The volume of the frustum will be expressed as:

Vf = Volume of the larger cone - Volume of the smaller cone

The volume of the larger cone  = $\frac{1}{3} \pi (7.5)^2(11+8)$

• The volume of the larger cone = $\frac{1}{3} \pi (7.5)^2(19)$

• The volume of the smaller cone = $\frac{1}{3} \pi (3.5)^2(8)$

Taking the difference in volume:

Volume of the frustum = $\frac{1}{3} \pi (7.5)^2(19) - \frac{1}{3} \pi (3.5)^2(8)$

Therefore the expression that represents the volume of the frustum in cubic units is $\frac{1}{3} \pi (7.5)^2(19) - \frac{1}{3} \pi (3.5)^2(8)$$units^3$

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