Question

1. a cone has a radius of 5 inches and a height of 9 inches. find the volume of the cone in terms of π.

a. 225π
b. 75π
c. 30π
d. 90π

1. find the volume of the cone in terms of π.

(image of a cone with height 18 yd and radius 9 yd)

Explanation:

Step1: Recall the formula for the volume of a cone

The formula for the volume \( V \) of a cone is \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute the given values

Given that \( r = 5 \) inches and \( h=9 \) inches. Substitute these values into the formula:
\( V=\frac{1}{3}\pi(5)^{2}(9) \)
First, calculate \( (5)^{2}=25 \). Then, multiply \( 25 \) and \( 9 \): \( 25\times9 = 225 \). Now, multiply by \( \frac{1}{3} \): \( \frac{1}{3}\times225=75 \). So the volume \( V = 75\pi \) cubic inches.

For the second sub - question:

Step1: Identify the radius and height

From the diagram, the radius \( r = 9 \) yd and the height \( h = 18 \) yd.

Step2: Apply the volume formula

Using the formula \( V=\frac{1}{3}\pi r^{2}h \), substitute \( r = 9 \) and \( h = 18 \):
\( V=\frac{1}{3}\pi(9)^{2}(18) \)
First, calculate \( (9)^{2}=81 \). Then, multiply \( 81 \) and \( 18 \): \( 81\times18=1458 \). Now, multiply by \( \frac{1}{3} \): \( \frac{1}{3}\times1458 = 486 \). So the volume \( V=486\pi \) cubic yards.

Answer:

1. B. \( 75\pi \)
2. The volume of the cone is \( 486\pi \) cubic yards.