date:
prisms and cylinders
1-6: find the volume of each cylinder rounded to the nearest tenth!
1.
cylinder with radius 9 in and height 14 in
2.
cylinder with diameter 12 m and height 11 m
3.
cylinder with radius 5 mm and height 8 mm
4.
cylinder with radius 14 cm and height 20 cm
5.
cylinder with diameter 15 ft and height 12 ft
6.
cylinder with diameter 36 m and height 10 m

Question

Accepted Answer

### Problem 1: Cylinder with radius 9 in and height 14 in
# Explanation:
## Step1: Recall the formula for the volume of a cylinder, $ V = \pi r^2 h $, where $ r $ is the radius and $ h $ is the height.
## Step2: Substitute $ r = 9 $ in and $ h = 14 $ in into the formula.
$ V = \pi \times (9)^2 \times 14 $
## Step3: Calculate $ 9^2 = 81 $, then multiply by 14: $ 81 \times 14 = 1134 $
## Step4: Multiply by $ \pi $: $ V = 1134\pi \approx 1134 \times 3.1416 \approx 3562.6 $ (rounded to the nearest tenth)
# Answer:
$ 3562.6 $ cubic inches

### Problem 2: Cylinder with diameter 12 m (so radius $ r = \frac{12}{2} = 6 $ m) and height 11 m
# Explanation:
## Step1: Use the volume formula $ V = \pi r^2 h $.
## Step2: Substitute $ r = 6 $ m and $ h = 11 $ m.
$ V = \pi \times (6)^2 \times 11 $
## Step3: Calculate $ 6^2 = 36 $, then multiply by 11: $ 36 \times 11 = 396 $
## Step4: Multiply by $ \pi $: $ V = 396\pi \approx 396 \times 3.1416 \approx 1244.1 $ (rounded to the nearest tenth)
# Answer:
$ 1244.1 $ cubic meters

### Problem 3: Cylinder with radius 5 mm and height 8 mm
# Explanation:
## Step1: Use the volume formula $ V = \pi r^2 h $.
## Step2: Substitute $ r = 5 $ mm and $ h = 8 $ mm.
$ V = \pi \times (5)^2 \times 8 $
## Step3: Calculate $ 5^2 = 25 $, then multiply by 8: $ 25 \times 8 = 200 $
## Step4: Multiply by $ \pi $: $ V = 200\pi \approx 200 \times 3.1416 \approx 628.3 $ (rounded to the nearest tenth)
# Answer:
$ 628.3 $ cubic millimeters

### Problem 4: Cylinder with radius 14 cm and height 20 cm
# Explanation:
## Step1: Use the volume formula $ V = \pi r^2 h $.
## Step2: Substitute $ r = 14 $ cm and $ h = 20 $ cm.
$ V = \pi \times (14)^2 \times 20 $
## Step3: Calculate $ 14^2 = 196 $, then multiply by 20: $ 196 \times 20 = 3920 $
## Step4: Multiply by $ \pi $: $ V = 3920\pi \approx 3920 \times 3.1416 \approx 12315.0 $ (rounded to the nearest tenth)
# Answer:
$ 12315.0 $ cubic centimeters

### Problem 5: Cylinder with diameter 15 ft (so radius $ r = \frac{15}{2} = 7.5 $ ft) and height 12 ft
# Explanation:
## Step1: Use the volume formula $ V = \pi r^2 h $.
## Step2: Substitute $ r = 7.5 $ ft and $ h = 12 $ ft.
$ V = \pi \times (7.5)^2 \times 12 $
## Step3: Calculate $ 7.5^2 = 56.25 $, then multiply by 12: $ 56.25 \times 12 = 675 $
## Step4: Multiply by $ \pi $: $ V = 675\pi \approx 675 \times 3.1416 \approx 2120.6 $ (rounded to the nearest tenth)
# Answer:
$ 2120.6 $ cubic feet

### Problem 6: Cylinder with diameter 36 m (so radius $ r = \frac{36}{2} = 18 $ m) and height 10 m
# Explanation:
## Step1: Use the volume formula $ V = \pi r^2 h $.
## Step2: Substitute $ r = 18 $ m and $ h = 10 $ m.
$ V = \pi \times (18)^2 \times 10 $
## Step3: Calculate $ 18^2 = 324 $, then multiply by 10: $ 324 \times 10 = 3240 $
## Step4: Multiply by $ \pi $: $ V = 3240\pi \approx 3240 \times 3.1416 \approx 10178.8 $ (rounded to the nearest tenth)
# Answer:
$ 10178.8 $ cubic meters

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: Cylinder with radius 9 in and height 14 in

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

Step2: Substitute \( r = 9 \) in and \( h = 14 \) in into the formula.

Step3: Calculate \( 9^2 = 81 \), then multiply by 14: \( 81 \times 14 = 1134 \)

Step4: Multiply by \( \pi \): \( V = 1134\pi \approx 1134 \times 3.1416 \approx 3562.6 \) (rounded to the nearest tenth)

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

Step2: Substitute \( r = 6 \) m and \( h = 11 \) m.

Step3: Calculate \( 6^2 = 36 \), then multiply by 11: \( 36 \times 11 = 396 \)

Step4: Multiply by \( \pi \): \( V = 396\pi \approx 396 \times 3.1416 \approx 1244.1 \) (rounded to the nearest tenth)

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

Step2: Substitute \( r = 5 \) mm and \( h = 8 \) mm.

Step3: Calculate \( 5^2 = 25 \), then multiply by 8: \( 25 \times 8 = 200 \)

Step4: Multiply by \( \pi \): \( V = 200\pi \approx 200 \times 3.1416 \approx 628.3 \) (rounded to the nearest tenth)

Answer:

Problem 2: Cylinder with diameter 12 m (so radius \( r = \frac{12}{2} = 6 \) m) and height 11 m