i can use formulas for volume to solve mathematical problems.
11 find the volume of a hemisphere with a radius of 7 inches. round to the nearest tenth.
12 a sphere - shaped snow globe has a radius of 3.5 inches. how much water can the snow globe hold? round to the nearest tenth.
the questions below give a description of a sphere. match each description with the volume of the sphere in terms of π. not all choices will be used.
13 a sphere with a radius of 18 units
14 a sphere with a diameter of 24 units
15 a sphere with a diameter of 18 units
16 a sphere with a radius of 15 units
a. 472π
b. 7,776π
c. 1,230π
d. 4,500π
e. 2,304π
17 a cone - shaped funnel can hold 314 cubic inches of water. if the height of the funnel is 12 inches, what is the radius of the funnel? use 3.14 for pi.
18 a cylindrical vase is filled with soil. if the height of the vase is 6 centimeters and the vase holds 471 cubic centimeters, what is the diameter of the vase? use 3.14 for pi.
19 the volume of a sphere is 36,000π units³. what is the radius of the sphere?

Question

Accepted Answer

11.
# Explanation:
## Step1: Recall volume formula for sphere
The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$. Given $r = 2$ inches.
## Step2: Substitute radius into formula
$V=\frac{4}{3}\pi(2)^{3}=\frac{4}{3}\pi	imes8=\frac{32}{3}\pi\approx33.5$ cubic - inches (rounded to the nearest tenth).

12.
# Explanation:
## Step1: Use volume formula for sphere
The volume formula of a sphere is $V=\frac{4}{3}\pi r^{3}$, with $r = 3.5$ inches.
## Step2: Calculate volume
$V=\frac{4}{3}\pi(3.5)^{3}=\frac{4}{3}\pi	imes42.875\approx179.6$ cubic - inches (rounded to the nearest tenth).

13.
# Explanation:
## Step1: Apply volume formula for sphere
The volume formula of a sphere is $V=\frac{4}{3}\pi r^{3}$, and $r = 18$ units.
## Step2: Compute volume
$V=\frac{4}{3}\pi(18)^{3}=\frac{4}{3}\pi	imes5832 = 7776\pi$.

14.
# Explanation:
## Step1: Find radius from diameter
Given diameter $d = 24$ units, then radius $r=\frac{d}{2}=12$ units.
## Step2: Use volume formula
$V=\frac{4}{3}\pi r^{3}=\frac{4}{3}\pi(12)^{3}=\frac{4}{3}\pi	imes1728 = 2304\pi$.

15.
# Explanation:
## Step1: Determine radius from diameter
Given diameter $d = 18$ units, so radius $r=\frac{d}{2}=9$ units.
## Step2: Calculate volume
$V=\frac{4}{3}\pi r^{3}=\frac{4}{3}\pi(9)^{3}=\frac{4}{3}\pi	imes729 = 972\pi$.

16.
# Explanation:
## Step1: Apply volume formula for sphere
The volume formula of a sphere is $V=\frac{4}{3}\pi r^{3}$, with $r = 15$ units.
## Step2: Compute volume
$V=\frac{4}{3}\pi(15)^{3}=\frac{4}{3}\pi	imes3375 = 4500\pi$.

17.
# Explanation:
## Step1: Recall volume formula for cone
The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Given $V = 314$ cubic inches and $h = 12$ inches.
## Step2: Substitute values and solve for $r$
$314=\frac{1}{3}\pi r^{2}(12)$. First, simplify the right - hand side: $\frac{1}{3}	imes12\pi r^{2}=4\pi r^{2}$. Then, since $\pi = 3.14$, we have $314 = 4	imes3.14r^{2}$. So, $314=12.56r^{2}$. Divide both sides by $12.56$: $r^{2}=\frac{314}{12.56}=25$. Then $r = 5$ inches.

18.
# Explanation:
## Step1: Recall volume formula for cylinder
The volume formula of a cylinder is $V=\pi r^{2}h$. Given $V = 471$ cubic centimeters and $h = 6$ centimeters.
## Step2: Substitute values and solve for $r$
$471=\pi r^{2}(6)$. Since $\pi = 3.14$, we have $471=3.14	imes6r^{2}=18.84r^{2}$. Divide both sides by $18.84$: $r^{2}=\frac{471}{18.84}=25$. So, $r = 5$ centimeters, and the diameter $d = 2r=10$ centimeters.

19.
# Explanation:
## Step1: Set up equation using volume formula for sphere
The volume formula of a sphere is $V=\frac{4}{3}\pi r^{3}$. Given $V = 36000\pi$ units³.
## Step2: Solve for $r$
$36000\pi=\frac{4}{3}\pi r^{3}$. First, cancel out $\pi$ on both sides: $36000=\frac{4}{3}r^{3}$. Multiply both sides by $\frac{3}{4}$: $r^{3}=36000	imes\frac{3}{4}=27000$. Then $r = 30$ units.

# Answer:
11. Approximately $33.5$ cubic inches
12. Approximately $179.6$ cubic inches
13. $7776\pi$
14. $2304\pi$
15. $972\pi$
16. $4500\pi$
17. $r = 5$ inches
18. $d = 10$ centimeters
19. $r = 30$ units

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall volume formula for sphere

Step2: Substitute radius into formula

Step1: Use volume formula for sphere

Step2: Calculate volume

Step1: Apply volume formula for sphere

Step2: Compute volume

Answer: