solve each of the problems below. be sure to ask questions if you need more help with a topic.
i can use a formula to find the volume of cylinders.
1. what is the formula used to find the volume of a cylinder? describe the steps to find the volume of a cylinder in your own words.
2. find the volume of the cylinder. leave your answer in terms of π. r = 8 mm, h = 24 mm
3. find the volume of the cylinder to the nearest tenth. d = 15 in, h = 11 in
4. a cylindrical can has a radius of 5.5 cm and a height of 8 cm. what is the capacity of the can to the nearest hundredth?
i can use a formula to find the volume of cones.
5. laura is trying to find the volume of a cone. so far, she has found the area of the base of the cone and multiplied it by the height of the cone. describe what she needs to do next.
6. a cylinder has a volume of 72 cubic inches. what is the volume of a cone with the same height and radius as the cylinder? explain.
7. find the volume of the cone in terms of π. d = 36, h = 30
8. find the volume of the cone to the nearest tenth. r = 2.5 in, h = 7 in
9. a cone has a diameter of 18 units and a slant height of 15 units. find the volume of the cone to the nearest hundredth.

Question

Accepted Answer

1.
# Explanation:
## Step1: Recall volume formula
The volume formula for a cylinder is $V=\pi r^{2}h$, where $r$ is the radius of the base and $h$ is the height of the cylinder. First, find the area of the circular - base ($A = \pi r^{2}$) and then multiply it by the height of the cylinder.
# Answer:
$V=\pi r^{2}h$

2.
# Explanation:
## Step1: Identify values
Given $r = 8$ mm and $h=24$ mm.
## Step2: Substitute into formula
$V=\pi r^{2}h=\pi	imes(8)^{2}	imes24=\pi	imes64	imes24 = 1536\pi$ $mm^{3}$
# Answer:
$1536\pi$ $mm^{3}$

3.
# Explanation:
## Step1: Find radius
Given $d = 15$ in, so $r=\frac{d}{2}=\frac{15}{2}=7.5$ in and $h = 11$ in.
## Step2: Use volume formula
$V=\pi r^{2}h=\pi	imes(7.5)^{2}	imes11=\pi	imes56.25	imes11 = 618.75\pi\approx1943.8$ $in^{3}$
# Answer:
$1943.8$ $in^{3}$

4.
# Explanation:
## Step1: Identify values
Given $r = 5.5$ cm and $h = 8$ cm.
## Step2: Apply formula
$V=\pi r^{2}h=\pi	imes(5.5)^{2}	imes8=\pi	imes30.25	imes8=242\pi\approx759.22$ $cm^{3}$
# Answer:
$759.22$ $cm^{3}$

5.
# Explanation:
## Step1: Recall cone - volume formula
The volume formula for a cone is $V=\frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height. Since she has found $Bh$, she needs to divide the result by 3.
# Answer:
She needs to divide the result by 3.

6.
# Explanation:
## Step1: Recall relationship
The volume of a cone with the same radius and height as a cylinder is $\frac{1}{3}$ of the volume of the cylinder.
## Step2: Calculate volume of cone
Given $V_{cylinder}=72$ cubic inches, so $V_{cone}=\frac{1}{3}	imes V_{cylinder}=\frac{1}{3}	imes72 = 24$ cubic inches.
# Answer:
$24$ cubic inches

7.
# Explanation:
## Step1: Identify values
Given $d = 36$, so $r = 18$ and $h = 30$.
## Step2: Use cone - volume formula
$V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi	imes(18)^{2}	imes30=\frac{1}{3}\pi	imes324	imes30 = 3240\pi$
# Answer:
$3240\pi$

8.
# Explanation:
## Step1: Identify values
Given $r = 2.5$ in and $h = 7$ in.
## Step2: Apply cone - volume formula
$V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi	imes(2.5)^{2}	imes7=\frac{1}{3}\pi	imes6.25	imes7=\frac{43.75\pi}{3}\approx45.7$ $in^{3}$
# Answer:
$45.7$ $in^{3}$

9.
# Explanation:
## Step1: Find radius
Given $d = 18$ units, so $r=\frac{d}{2}=9$ units. Use the Pythagorean theorem to find the height $h$. Since $l = 15$ units (slant - height) and $r = 9$ units, $h=\sqrt{l^{2}-r^{2}}=\sqrt{15^{2}-9^{2}}=\sqrt{225 - 81}=\sqrt{144}=12$ units.
## Step2: Calculate volume
$V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi	imes(9)^{2}	imes12=\frac{1}{3}\pi	imes81	imes12 = 324\pi\approx1017.88$ $units^{3}$
# Answer:
$1017.88$ $units^{3}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall volume formula

Step1: Identify values

Step2: Substitute into formula

Step1: Find radius

Step2: Use volume formula

Answer: