Question

Let V be the volume of a right circular cone of height h=14 whose base is a circle of radius R=2. An illustration a right circular cone with horizontal cross sections. The right circular cone has a line segment from the center of the base to a point on the circle of the base is labeled capital R, and the horizontal line from the vertex is labeled h.
Required:
Use similar triangles to find the area of a horizontal cross section at a height y.

Answer 1

Answer:

The area of a horizontal cross section at a height is $\pi\times(2-\dfrac{y}{7})^2$

Step-by-step explanation:

Given that,

Height = 14 m

Radius = 2 m

Let V be the volume of a right circular cone

We need to calculate the value of R

Using given data

$\dfrac{h}{r}=\dfrac{h-y}{R}$

Put the value into the formula

$\dfrac{14}{2}=\dfrac{14-y}{R}$

$7R=14-y$

$R=2-\dfrac{y}{7}$

We need to calculate the area of a horizontal cross section at a height y

Using formula of area

$A=\pi R^2$

Put the value into the formula

$A=\pi\times(2-\dfrac{y}{7})^2$

Hence, The area of a horizontal cross section at a height is $\pi\times(2-\dfrac{y}{7})^2$