Question

A godown building is in the form as shown in figure. The vertical cross-section parallel to the width side of the building is a rectangle $7m\times 3m$, mounted by a semi-circle of radius $3.5m$. The inner measurements of the cuboidal portion of the building are $10m\times 7m\times 3m$. Find the volume of the godown and the total interior surface area excluding the floor (Base). (Take $\pi =22/7$)

Answer 1

Since the top of the building is in the form of half of the cylinder of radius $3.5m$, and length $10m$, split along the diameter

$V=$ volume of the godown
$V=$ Volume of the cuboid $+\frac{1}{2}$ (Volume of the cylinder of radius $3.5m$ and length $10m$)

$=(l\times b\times h)+\frac{1}{2}\left(\pi r^{2}h\right)$

$=\{10\times 7\times 3+\frac{1}{2}(\frac{22}{7}\times 3.5\times 3.5\times 10)\}{m}^3=(210+192.5)m^3=402.5m^3$

total surface area excluding the base floor

$=$Area of four walls +$\frac{1}{2}$ Curved surface area of the cylinder + 2 area of the semi-circles

$=[2(10+7)\times 3\times \frac{1}{2}(\frac{22}{7}\times 3.5\times 3.5\times 10)+2(\frac{22}{7}\times 3.5\times 3.5)]m^2$

$=250.5m^2$