Question

The shape of a solid is a cylinder surmounted by a cone. If the volume of the solid is $40656c{m}^3$, the diameter of the base is $42cm$ and the height of the cylinder is $20cm$, find the slant height of the conical portion.

• A. $45cm$
• B. $35cm$
• C. $40cm$
• D. $50cm$

Answer 1

The correct option is B $35cm$

Volume of the solid $=$ Volume of the cylindrical part $+$ Volume of conical part

Volume of a Cylinder of Radius "r" and height "h" $=\pi r^{2}h$
Volume of a cone $=\frac{1}{3}\pi r^{2}h$ where ris the radius of the base of the cone and h is the height.
Radius of the cone and cylinder $=\frac{42}{2}=21cm$

Hence, Volume of the solid $=(\frac{22}{7}\times 21\times 21\times 20)+(\frac{1}{3}\times \frac{22}{7}\times 21\times 21\times h)=40656$

$\Rightarrow 27720+462h=40656$

$\Rightarrow 462h=12936$

$\Rightarrow h=28cm$

For a cone, $l=\sqrt{h^2+r^2}$ where $l$ is the slant height.

Hence, $l=\sqrt{{28}^2+{21}^2}$

$l=\sqrt{1225}$

$l=35cm$