A cone has base radius = 4 cm and height = 2 cm.Using horizontal slicing, which of the following definite integrals represents volume of the cone? A) $\int_{0}^{2} 6 \pi h^{2} d h$ cm³ B) $\int_{0}^{2} \pi(4-2 h)^{2} d h$ cm³ C) $\int_{0}^{4} \pi(2-h)^{2} d h$ cm³ D) $\int_{0}^{-4} \pi(4-h)^{2} d h$ cm³

Question

Quizplus · Accepted Answer

The volume of a cone using horizontal slicing is given by the integral $\int_{0}^{h} \pi r(h)^{2} dh$, where r(h) is the radius of the cross-section at height h. In this case, the radius of the cross-section at height h is 4 - 2h, so the integral becomes $\int_{0}^{2} \pi(4-2 h)^{2} d h$.

A Cone Has Base Radius = 4 Cm and Height ∫026πh2dh\int_{0}^{2} 6 \pi h^{2} d h∫02​6πh2dh

A Cone Has Base Radius = 4 Cm and Height $\int_{0}^{2} 6 \pi h^{2} d h$