Question

The interior of a building is in the form of a cylinder of base radius $12m$ and height $3.5m$ surmounted by a cone of equal base and slant height $12.5m$. Find the internal curved surface are and the capacity of the building.

Answer 1

Internal CSA$=2\pi rH+\pi rl$

$=\pi r[2h+l]$

$=\frac{22}{7}\times 12[2\times 3.5+12.5]$

$=\frac{22}{7}\times 12\times 19.5=735.43m^3$

Capacity of building$=\frac{1}{3}\pi r^{2}h+\pi r^{2}H$

$=\pi r^2[\frac{1}{3}\sqrt{l^2-r^2}+H]=\frac{22}{7}\times {12}^2[\frac{1}{3}\sqrt{{12.5}^2-{12}^2}+3.5]$

$=\frac{22}{7}\times 144[\frac{3.5}{3}+3.5]=2112m^3$