A tower is topped by a hemispherical dome that has a surface area of 363$$\pi$$​ m sq.ft approximately. Find the volume of the dome (in cubic ft ).

Correct option is B

Given:

Total Surface area of hemisphere =363π sqft

Formula Used:

Total Surface Area of hemisphere =  $$3\pi r^2$$​​

Volume of hemisphere = $$\frac{2}{3}\pi r^3$$​​

Solution:

Here surface area  =363$$\pi$$​sqft

​$$3 \pi r^2 = 363\pi$$​​

​$$3 \times r^2 = 363$$​​

​$$r^2 =121$$​​

​$$r = \sqrt{121}$$​

​$$r=11 ft$$​​

Volume of dome = $$\frac{2}{3} \pi (11)^3$$​​

=  $$\frac{2}{3} \pi \times 1331$$​​

= $$887.3\pi \ ft^3$$​​