What is represented by the integral $\int_{0}^{4} \pi\left(\frac{x}{2}\right)^{2} d x$ ?
A)A cone with radius 2 and height 4.
B)A cone with radius 4 and height 4.
C)A sphere with radius 4.
D)A hemisphere with radius 4.

Question

Quizplus · Accepted Answer

The integral represents the volume of a cone with a radius of 2 and height of 4, calculated using the formula for the volume of a cone, $V = \frac{1}{3}\pi r^2 h$, where the integral calculates the area of circles with radii growing from 0 to 2 as x moves from 0 to 4, effectively stacking these to form a cone.

What Is Represented by the Integral ∫04π(x2)2dx\int_{0}^{4} \pi\left(\frac{x}{2}\right)^{2} d x∫04​π(2x​)2dx ? A)A Cone with Radius 2 and Height 4

What Is Represented by the Integral $\int_{0}^{4} \pi\left(\frac{x}{2}\right)^{2} d x$ ?
A)A Cone with Radius 2 and Height 4