Question

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. The heap is to be covered by canvas to protect it from the rain. Find the volume of the heap and the area of the canvas required.

• A. $86.625m^3$, $99.825m^2$
• B. $99.625m^3$, $86.825m^2$
• C. $99.625m^3$, $56.825m^2$
• D. $26.625m^3$, $86.825m^2$

Answer 1

The correct option is A $86.625m^3$, $99.825m^2$

Radius (r) of the heap $=\left(\frac{10.5}{2}\right)m=5.25m$
Height (h) of heap = 3 m
Volume of the heap $=\frac{1}{3}\pi r^{2}h$
$=(\frac{1}{3}\times \frac{22}{7}\times (5.25{)}^2\times 3)m^3$
$=86.625m^3$
Therefore, the volume of the heap of wheat is $86.625m^3$.
Area of canvas required = CSA of cone
$=\pi rl=\pi r\sqrt{r^2+h^2}$
$=[\frac{22}{7}\times 5.25\times \sqrt{(5.25{)}^2+(3{)}^2}]m^2$
$=(\frac{22}{7}\times 5.25\times 6.05)m^2$
$=99.825m^2$
Therefore $99.825m^2$ of canvas will be required to protect the heap from the rain.