Find the volume of a sphere with a radius of 1.8 yards. Leave your answer in terms of pi. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses
7.78π yds3
7.78 pi yds cubed
7.2π yds3
7.2 pi yds cubed
23.34π yds3
23.34 pi yds cubed
24.43π yds3
The volume V of a sphere with radius r is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
Given that the radius is 1.8 yards, we can substitute r with 1.8 yards into the formula to find the volume:
\[ V = \frac{4}{3} \pi (1.8)^3 \]
\[ V = \frac{4}{3} \pi (5.832) \] (since 1.8^3 = 5.832 exactly)
\[ V = 7.776 \pi \]
Rounding to the nearest hundredth, we get:
\[ V \approx 7.78 \pi \, \text{yds}^3 \]
So, the volume of the sphere in terms of pi, rounded to the nearest hundredth, is approximately \( 7.78 \pi \) cubic yards.
Use the formula for the volume of a sphere to solve the following problem.
How much air is needed to fill a basketball with a diameter of 9 inches? Use 3.14 as an approximation for pi. Round your answer to the nearest tenth.
(1 point)
Responses
113 in.3
113 inches cubed
381.5 in.3
381.5 inches cubed
190.8 in.3
190.8 inches cubed
3,052.1 in.3