Question

Цилиндр описан около шара. Объём цилиндра равен 78. Найдите объём шара

Answer 1

R3=78÷2 pi=36÷pi

Отсюда обьём шара

V(шара)=(4 pi*36)÷3pi=4*12=48см2

Answer 2

I will answer in detail. A cylinder is circumscribed around a sphere. The volume of the cylinder is 78. Find the volume of the sphere.

If a cylinder is circumscribed around a sphere, then the radius of the sphere is equal to the radius of the base of the cylinder, and the height of the cylinder is equal to twice the radius of the sphere. Therefore, we can use the formula for the volume of a cylinder to find the radius of the sphere:

$$V_{\text{cyl}}=\pi R^2 H$$

$$78=\pi R^2 \cdot 2R$$

$$R^3=\frac{78}{2\pi}$$

Then, we can use the formula for the volume of a sphere to find the volume of the sphere:

$$V_{\text{sph}}=\frac{4}{3}\pi R^3$$

$$V_{\text{sph}}=\frac{4}{3}\pi \cdot \frac{78}{2\pi}$$

$$V_{\text{sph}}=\frac{52}{\pi}$$

Answer: The volume of the sphere is $\frac{52}{\pi}$.

This solution is similar to the one given in [this website](https://ege.sdamgia.ru/problem?id=269289), but with different numbers. You can also check [other sources](https://neznaika.info/q/21482) for more examples and explanations.