Question

1. a cylinder has a radius of 7 inches and a height of 10 inches. what is the volume of the cylinder?

a. (210pi) in³
b. (490pi) in³
c. (700pi) in³
d. (4900pi) in⁴

1. a cylindrical pipe has an outer radius of 6 cm and an inner radius of 4 cm. if the height is 14 cm, what is the volume of the material that makes up the pipe?

a. (280pi) cm³
b. (560pi) cm³
c. (112pi) cm³
d. (224pi) cm³

1. if a cylinders volume is (100pi) cubic units and the height is 5 units, what is the radius of its base?

a. 5.25
b. 2.14
c. 4.47
d. 10

1. what does the

\ represent in the formula (v = pi r^2 h)?
a. height
b. diameter of the base
c. area of the base
d. radius of the base

Explanation:

Problem 1

Step1: Recall cylinder volume formula

$V = \pi r^2 h$

Step2: Substitute $r=7, h=30$

$V = \pi \times 7^2 \times 30 = \pi \times 49 \times 30 = 1470\pi$

Problem 2

Step1: Use hollow cylinder volume formula

$V = \pi (R^2 - r^2) h$

Step2: Substitute $R=6, r=4, h=14$

$V = \pi \times (6^2 - 4^2) \times 14 = \pi \times (36-16) \times 14 = \pi \times 20 \times 14 = 280\pi$

Problem 3

Step1: Rearrange volume formula for $r$

$r = \sqrt{\frac{V}{\pi h}}$

Step2: Substitute $V=100\pi, h=5$

$r = \sqrt{\frac{100\pi}{\pi \times 5}} = \sqrt{20} \approx 4.47$

Problem 4

Step1: Analyze $V=\pi r^2 h$ components

In $\pi r^2 h$, $\pi r^2$ is the area of the circular base, so $\pi r^2$ represents the base area.

Answer:

1. c. $1470\pi \text{ in}^3$
2. a. $280\pi \text{ cm}^3$
3. c. 4.47
4. c. Area of the base