Question

4. The function V (r) = 10πr^2 represents the volume of a cylinder that is 10 inches high with a radius of r. Which is the correct interpretation for the function notation V (3) = 90π
A) The volume of the cylinder is 90𝜋 when the radius is 3.
B) A cylinder of 90𝜋 is produced from a radius of 3.
C) A radius of 3 gives the value 90.
D) The volume of the cylinder is 3 when the radius is 90𝜋.

5. Monique is punting a football and the height the ball travels is a function of time. The function h(s) = −s^2 + 10s + 3 gives the height of the ball, h(s), given the number of seconds, 𝑠 that the ball has been in the air. After flying through the air for 7.5 seconds, what is the height of the ball? Find ℎ (7.5)
A) 134.25
B) 21.75
C) 24
D) 21.5

Answer 1

Let's solve each question step by step.

**Question 4:** The function \( V(r) = 10\pi r^2 \) represents the volume of a cylinder with height 10 inches and radius \( r \). We need to interpret \( V(3) = 90\pi \).

To find \( V(3) \):
\[
V(3) = 10\pi(3^2) = 10\pi(9) = 90\pi
\]

Now, we can interpret the result:
- **A)** The volume of the cylinder is \( 90\pi \) when the radius is \( 3 \). (This is correct.)
- **B)** A cylinder of \( 90\pi \) is produced from a radius of 3. (This wording is a bit ambiguous.)
- **C)** A radius of 3 gives the value 90. (This is incorrect; it gives \( 90\pi \), not 90.)
- **D)** The volume of the cylinder is 3 when the radius is \( 90\pi \). (This is incorrect.)

The correct answer is **A)**.

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**Question 5:** We have the function \( h(s) = -s^2 + 10s + 3 \), and we want to find \( h(7.5) \).

Calculating \( h(7.5) \):
\[
h(7.5) = -(7.5)^2 + 10(7.5) + 3
\]
Calculating each component:
\[
(7.5)^2 = 56.25 \quad \text{so} \quad -56.25
\]
\[
10(7.5) = 75
\]
Adding it all together:
\[
h(7.5) = -56.25 + 75 + 3
\]
\[
= -56.25 + 78
\]
\[
= 21.75
\]

Thus, the height of the ball after 7.5 seconds is **B)** 21.75.