Question

spheres and cylinders 2
find the volume of each figure. round your answers to the nearest hundredth, if necessary.
1)
20 in
2)
1 mi
3)
1.5 ft
4)
18 km
5)
24 m
6)
10 yd
9 yd
7)
8 cm
12 cm
8)
6 km
8 km
9)
9 mi
10 mi
10)
6 in
3 in

Explanation:

Step1: Identify the figure (Sphere or Cylinder)

For problem 1, the figure is a sphere (indicated by a single circle with a radius). The formula for the volume of a sphere is \( V = \frac{4}{3}\pi r^3 \), where \( r \) is the radius.

Step2: Substitute the radius value

The radius \( r = 20 \) in. Substitute into the formula: \( V = \frac{4}{3}\pi (20)^3 \)

Step3: Calculate the volume

First, calculate \( 20^3 = 8000 \). Then, \( \frac{4}{3}\pi \times 8000 = \frac{32000}{3}\pi \approx \frac{32000}{3} \times 3.1416 \approx 33510.32 \) cubic inches.

(Repeat similar steps for other problems. For cylinders, the formula is \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.)

Answer:

For problem 1 (Sphere, \( r = 20 \) in): \( \approx 33510.32 \) in³
(For other problems, follow the same method with respective formulas and dimensions. For example, problem 6: Cylinder, \( r = 9 \) yd, \( h = 10 \) yd, \( V = \pi \times 9^2 \times 10 = 810\pi \approx 2544.69 \) yd³; problem 7: Cylinder, \( r = 8 \) cm, \( h = 12 \) cm, \( V = \pi \times 8^2 \times 12 = 768\pi \approx 2412.74 \) cm³, etc.)