Find the volume (in cm³) of a cylinder that circumscribes a sphere with a radius of 2.8 cm. $$\Big(Use \pi = \frac{22}{7}\Big)$$​​​

Correct option is A

Given:

The radius of the sphere is 2.8 cm.

Therefore, the diameter of the sphere is 2×2.8=5.6cm. 

Concept Used: 

A cylinder that circumscribes a sphere means that the sphere fits perfectly inside the cylinder, touching both the bottom and the top of the cylinder, as well as the sides.

Formula Used:

The volume VVV of a cylinder is given by the formula:

$$V = \pi r^2 h$$ 

Where:

r is the radius of the cylinder's base,

h is the height of the cylinder,

π is approximately 22/7 (as given in the problem).

Solution:

Radius of the cylinder's base (r) is the same as the radius of the sphere, so r = 2.8cm.

Height of the cylinder (h) is equal to the diameter of the sphere, so h = 5.6cm.

Now, substitute these values into the volume formula: 

$$V = \frac{22}{7} \times (2.8)^2 \times 5.6$$ 

$$V = \frac{22}{7} \times7.84 \times 5.6$$ 

$$V = 22 \times 1.12 \times 5.6$$ 

$$V = 137.984 cm^3$$ 

Thus, the volume of the cylinder is approximately 137.984 $$cm^3$$.

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