Question

question 4 2 pts a cylinder having a diameter of 7 inches and a depth of 25 inches has a volume of (2 decimals) question 4 2 pts a sphere with a circumference of 41 inches has the volume of: (2 decimals) question 5 5 pts

Explanation:

Step1: Find radius of cylinder

Given diameter $d = 7$ inches, radius $r=\frac{d}{2}=\frac{7}{2}=3.5$ inches.

Step2: Calculate volume of cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$. Here $h = 25$ inches. So $V=\pi\times(3.5)^{2}\times25=\pi\times12.25\times25 = 306.25\pi\approx962.11$ cubic - inches.

Step3: Find radius of sphere

Given circumference $C = 41$ inches. Since $C = 2\pi r$, then $r=\frac{C}{2\pi}=\frac{41}{2\pi}$ inches.

Step4: Calculate volume of sphere

The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = \frac{41}{2\pi}$ into the formula:
\[

$$\begin{align*} V&=\frac{4}{3}\pi\times(\frac{41}{2\pi})^{3}\\ &=\frac{4}{3}\pi\times\frac{41^{3}}{8\pi^{3}}\\ &=\frac{41^{3}}{6\pi^{2}}\\ &=\frac{68921}{6\pi^{2}}\\ &\approx370.77 \end{align*}$$

\]

Answer:

Question 4 (cylinder): 962.11
Question 5 (sphere): 370.77