Question

i can use a formula to find the volume of spheres. 10. find the volume of the sphere. round to the nearest tenth. 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. 972π b. 7,776π c. 1,230π d. 4,500π e. 2,304π i can use formulas for volume to solve mathematical problems. 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?

Explanation:

Step1: Recall volume formula for sphere

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$, where $r$ is the radius of the sphere.

Step2: Solve problem 10

Given diameter $d = 22$, then radius $r=\frac{d}{2}=11$. Substitute $r = 11$ into the formula: $V=\frac{4}{3}\pi(11)^{3}=\frac{4}{3}\pi\times1331=\frac{5324\pi}{3}\approx5575.3$ (rounded to nearest tenth).

Step3: Solve problem 11

For a hemisphere, the volume formula is $V=\frac{2}{3}\pi r^{3}$. Given $r = 7$, then $V=\frac{2}{3}\pi(7)^{3}=\frac{2}{3}\pi\times343=\frac{686\pi}{3}\approx718.4$ (rounded to nearest tenth).

Step4: Solve problem 12

Given $r = 3.5$, substitute into sphere - volume formula $V=\frac{4}{3}\pi(3.5)^{3}=\frac{4}{3}\pi\times42.875=\frac{171.5\pi}{3}\approx179.6$ (rounded to nearest tenth).

Step5: Solve problem 13

Given $r = 18$, $V=\frac{4}{3}\pi(18)^{3}=\frac{4}{3}\pi\times5832 = 7776\pi$.

Step6: Solve problem 14

Given $d = 24$, then $r = 12$. $V=\frac{4}{3}\pi(12)^{3}=\frac{4}{3}\pi\times1728 = 2304\pi$.

Step7: Solve problem 15

Given $d = 18$, then $r = 9$. $V=\frac{4}{3}\pi(9)^{3}=\frac{4}{3}\pi\times729 = 972\pi$.

Step8: Solve problem 16

Given $r = 15$, $V=\frac{4}{3}\pi(15)^{3}=\frac{4}{3}\pi\times3375 = 4500\pi$.

Step9: Solve problem 17

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Given $V = 314$ and $h = 12$. Substitute into the formula: $314=\frac{1}{3}\pi r^{2}(12)$. First, simplify the right - hand side: $\frac{1}{3}\times12\pi r^{2}=4\pi r^{2}$. Then $r^{2}=\frac{314}{4\pi}$. Since $\pi = 3.14$, $r^{2}=\frac{314}{4\times3.14}=25$, so $r = 5$.

Step10: Solve problem 18

The volume formula for a cylinder is $V=\pi r^{2}h$. Given $V = 471$ and $h = 6$. Substitute into the formula: $471=\pi r^{2}(6)$. Then $r^{2}=\frac{471}{6\pi}$. Since $\pi = 3.14$, $r^{2}=\frac{471}{6\times3.14}=25$, so $r = 5$ and $d = 10$.

Step11: Solve problem 19

Given $V = 36000\pi$, and $V=\frac{4}{3}\pi r^{3}$. Then $36000\pi=\frac{4}{3}\pi r^{3}$. Cancel out $\pi$ on both sides: $36000=\frac{4}{3}r^{3}$. Multiply both sides by $\frac{3}{4}$: $r^{3}=27000$, so $r = 30$.

Answer:

1. $5575.3$
2. $718.4$
3. $179.6$
4. B. $7776\pi$
5. E. $2304\pi$
6. A. $972\pi$
7. D. $4500\pi$
8. $5$
9. $10$
10. $30$