Question

directions: solve for the volume of the figure below. show your solution step by step. write your answer on 1/2 sheet of paper. round your answer to the nearest hundredths. (3 points each)

Explanation:

Step1: Recall volume formula for sphere

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$, where $r$ is the radius of the sphere.

Step2: Solve for problem 1

Given $r = 2.4m$. Substitute into the formula:
$V_1=\frac{4}{3}\pi(2.4)^{3}=\frac{4}{3}\pi\times13.824\approx\frac{4}{3}\times3.14\times13.824\approx57.91m^{3}$

Step3: Solve for problem 2

Given diameter $d = 30mm$, so $r=\frac{d}{2}=15mm$. Then $V_2=\frac{4}{3}\pi(15)^{3}=\frac{4}{3}\pi\times3375\approx\frac{4}{3}\times3.14\times3375 = 14130.00mm^{3}$

Step4: Solve for problem 3

Given $r = 8.2in$. Substitute into the formula:
$V_3=\frac{4}{3}\pi(8.2)^{3}=\frac{4}{3}\pi\times551.368\approx\frac{4}{3}\times3.14\times551.368\approx2308.43in^{3}$

Step5: Solve for problem 4

Given $r = 10cm$. Substitute into the formula:
$V_4=\frac{4}{3}\pi(10)^{3}=\frac{4}{3}\pi\times1000\approx\frac{4}{3}\times3.14\times1000\approx4186.67cm^{3}$

Step6: Solve for problem 5

Given diameter $d = 1m$, so $r=\frac{d}{2}=0.5m$. Then $V_5=\frac{4}{3}\pi(0.5)^{3}=\frac{4}{3}\pi\times0.125\approx\frac{4}{3}\times3.14\times0.125\approx0.52m^{3}$

Answer:

1. $V_1\approx57.91m^{3}$
2. $V_2 = 14130.00mm^{3}$
3. $V_3\approx2308.43in^{3}$
4. $V_4\approx4186.67cm^{3}$
5. $V_5\approx0.52m^{3}$