Question

Emmanuel carves a cone-shaped hollow out of a solid clay cylinder. What is the approximate volume of the solid portion of the cylinder? Use 3.14 for π.

Answer 1

Answer:

$3.14r^2(h-\frac{1}{3}h_1)$

Step-by-step explanation:

Let h be the cylinders height and r the radius.

-The volume of a cylinder is calculated as:

$V=\pi r^2h$

-Since the cone is within the cylinder, it has the same radius as the cylinder.

-Let $h_1$be the height of the cone.

-The area of a cone is calculated as;

$V=\pi r^2 \frac{h}{3}\\\\=\frac{1}{3}\pi r^2h_1$

The volume of the  solid section of the cylinder is calculated by subtracting the cone's volume from the cylinders:

$V=V_{cy}-V_{co}\\\\=\pi r^2h-\frac{1}{3}\pi r^2 h_1, \pi=3.14\\\\=3.14r^2(h-\frac{1}{3}h_1)$

Hence, the approximate area of the solid portion is $3.14r^2(h-\frac{1}{3}h_1)$