3 practice 3
find the volume of each solid. give exact answers.
a. a cylinder with radius 4 inches and height 3 inches
type your answer in the box.
______ cubic inches
b. a cylinder with radius 3 inches and height 4 inches
type your answer in the box.
______ cubic inches
c. a hexagonal prism whose base has area 30.5 square centimeters and whose height is 6.5 centimeters
type your answer in the box.
______ cubic centimeters
d. a prism 5 feet tall whose base is a right triangle with leg lengths 6 feet and 7 feet
type your answer in the box.
______ cubic feet
how did i do?

Question

Accepted Answer

### Part a
# Explanation:
## Step1: Recall the formula for the volume of a cylinder, which is $ V = \pi r^2 h $, where $ r $ is the radius and $ h $ is the height.
## Step2: Substitute $ r = 4 $ inches and $ h = 3 $ inches into the formula. So $ V=\pi\times(4)^2\times3=\pi\times16\times3 = 48\pi $.
# Answer:
$ 48\pi $

### Part b
# Explanation:
## Step1: Use the volume formula for a cylinder $ V = \pi r^2 h $.
## Step2: Substitute $ r = 3 $ inches and $ h = 4 $ inches. Then $ V=\pi\times(3)^2\times4=\pi\times9\times4 = 36\pi $.
# Answer:
$ 36\pi $

### Part c
# Explanation:
## Step1: The formula for the volume of a prism is $ V = B\times h $, where $ B $ is the area of the base and $ h $ is the height of the prism.
## Step2: Substitute $ B = 30.5 $ square centimeters and $ h = 6.5 $ centimeters. So $ V=30.5\times6.5 = 198.25 $.
# Answer:
$ 198.25 $

### Part d
# Explanation:
## Step1: First, find the area of the triangular base. The area of a right triangle is $ \frac{1}{2}\times\text{leg}_1\times\text{leg}_2 $. Here, legs are 6 feet and 7 feet, so $ B=\frac{1}{2}\times6\times7 = 21 $ square feet.
## Step2: Use the prism volume formula $ V = B\times h $, where $ h = 5 $ feet (height of the prism). Substitute $ B = 21 $ and $ h = 5 $, so $ V=21\times5 = 105 $.
# Answer:
$ 105 $

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QUESTION IMAGE

Question

Explanation:

Part a

Step1: Recall the formula for the volume of a cylinder, which is \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute \( r = 4 \) inches and \( h = 3 \) inches into the formula. So \( V=\pi\times(4)^2\times3=\pi\times16\times3 = 48\pi \).

Step1: Use the volume formula for a cylinder \( V = \pi r^2 h \).

Step2: Substitute \( r = 3 \) inches and \( h = 4 \) inches. Then \( V=\pi\times(3)^2\times4=\pi\times9\times4 = 36\pi \).

Step1: The formula for the volume of a prism is \( V = B\times h \), where \( B \) is the area of the base and \( h \) is the height of the prism.

Step2: Substitute \( B = 30.5 \) square centimeters and \( h = 6.5 \) centimeters. So \( V=30.5\times6.5 = 198.25 \).

Answer:

Part b