A conical vessel has base radius 31 cm and height 45 cm. Water is poured into the vessel until it is $$\frac{2}{3}$$ full. Find the volume (in cm³) of water in the vessel.​

Correct option is C

Given:

Cone base radius r = 31 cm

Cone height h = 45 cm

Vessel filled to $$\frac{2}{3}$$​ of its capacity

Formula Used:

Volume of a cone: V$$_{\text{cone}} = \dfrac{1}{3}\pi r^2 h$$​​

Solution:
​$$V_{\text{cone}}=\frac{1}{3}\pi(31)^2(45) \\ \ \\=\frac{1}{3}\pi(961)(45) \\ \ \\=\pi(961\times 15) \\ \ \\=14415\pi\ \text{cm}^3$$​​
$$V_{\text{water}} = \dfrac{2}{3}V_{\text{cone}}$$

​$$V_{\text{water}}=\frac{2}{3}\times 14415\pi=9610\pi\ \text{cm}^3$$​​