Question

a sphere of diameter 12 cm is dropped in a right circular cylindrical vessel partly filled with water. If the sphere is completely submerged in water the water level in the cylindrical vessel rises by 26/7cm .Find the diameter of the cylindrical vessel.​

Answer 1

Given,

• Radius of sphere (r) = 12cm

Let radius of cylinder be R and original height of water be h

∴ Volume of water = πR²h

Volume of sphere = 4/3πr³

When the sphere was dropped in vessel the water raised to 26/7 cm

⇒ $\bold{\mathff{\dfrac{4}{3}\pi r^3+\pi R^2h = \pi R^2\bigg(h+\dfrac{26}{7}\bigg)}}$

⇒$\bold{\mathff{\dfrac{4}{3}\pi r^3+\pi R^2h = \pi R^2h+\pi R^2\dfrac{26}{7}}}$

⇒ $\bold{\mathff{\dfrac{4}{3} r^3 = R^2\dfrac{26}{7}}}$

⇒ $\bold{\mathff{R^2= \dfrac{4 \times 7 \times r^3}{3 \times 26}= \dfrac{4 \times 7 \times 12^3}{3\times 26}}}$

R $\bold{\mathff{=\sqrt{620.307}=24.90}}$

R ≈ 25cm