Jevonte measure the volume of a sink basin by modeling it as a hemisphere. Jevonte mea
its radius to be inches. Find the sink’s volume in cubic inches. Round your answer to
nearest tenth if necessary.

Question

Jevonte measure the volume of a sink basin by modeling it as a hemisphere. Jevonte mea
its radius to be

inches. Find the sink’s volume in cubic inches. Round your answer to
nearest tenth if necessary.

UpStudy AI · Accepted Answer

To find the volume of the hemisphere, we can use the formula for the volume of a hemisphere:

$$ V = \frac{2}{3} \pi r^3 $$

Given that the radius of the hemisphere is $$ 12 \frac{3}{4} $$ inches, we can substitute this value into the formula to find the volume.

Substitute $$ r = 12 \frac{3}{4} $$ inches into the formula:

$$ V = \frac{2}{3} \pi (12 \frac{3}{4})^3 $$

Now, we can calculate the volume of the hemisphere.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{2}{3}\pi \left(12+\frac{3}{4}\right)^{3}$$
- step1: Add the numbers:
  $$\frac{2}{3}\pi \left(\frac{51}{4}\right)^{3}$$
- step2: Multiply:
  $$\frac{2\pi }{3}\left(\frac{51}{4}\right)^{3}$$
- step3: Evaluate the power:
  $$\frac{2\pi }{3}\times \frac{51^{3}}{4^{3}}$$
- step4: Rewrite the expression:
  $$\frac{2\pi }{3}\times \frac{51^{3}}{2^{6}}$$
- step5: Reduce the numbers:
  $$\frac{\pi }{3}\times \frac{51^{3}}{2^{5}}$$
- step6: Rewrite the expression:
  $$\frac{\pi }{3}\times \frac{3^{3}\times 17^{3}}{2^{5}}$$
- step7: Reduce the numbers:
  $$\pi \times \frac{3^{2}\times 17^{3}}{2^{5}}$$
- step8: Multiply:
  $$\frac{\pi \times 44217}{2^{5}}$$
- step9: Multiply:
  $$\frac{44217\pi }{2^{5}}$$
- step10: Evaluate the power:
  $$\frac{44217\pi }{32}$$
The volume of the hemisphere is approximately $$ 4340.993824 $$ cubic inches. Rounding this to the nearest tenth, the volume of the sink basin is approximately $$ 4341 $$ cubic inches.
The volume of the sink basin is approximately 4341 cubic inches.

Jevonte measure the volume of a sink basin by modeling it as a hemisphere. Jevonte mea
its radius to be inches. Find the sink’s volume in cubic inches. Round your answer to
nearest tenth if necessary.

Upstudy AI Solution

Answer

Solution

Mind Expander

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Latest Geometry Questions

Jevonte measure the volume of a sink basin by modeling it as a hemisphere. Jevonte mea its radius to be inches. Find the sink’s volume in cubic inches. Round your answer to nearest tenth if necessary.

Upstudy AI Solution

Answer

Solution

Mind Expander

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Latest Geometry Questions

Jevonte measure the volume of a sink basin by modeling it as a hemisphere. Jevonte mea
its radius to be inches. Find the sink’s volume in cubic inches. Round your answer to
nearest tenth if necessary.