Question

The curved surface area of a cone exceeds the base area by $88c{m}^2$. Its slant height exceeds the base radius by $4cm.$ Find the radius of the base.

Answer 1

It is given that curved surface area $(C.S.A)$ exceeds the Base area $\left(A\right)$ of cone by $88c{m}^2$

$\therefore C.S.A-A=88$

$\Rightarrow \pi rl-\pi r^2=88$ [$\because C.S.A$ of cone $=\pi rl$, Base area of cone $=\pi r^2$]

$\Rightarrow \pi r(l-r)=88\dots \dots \left(i\right)$

And, it is also given that slant height $\left(l\right)$ exceeds the base radius $\left(r\right)$ by $4cm.$

$\Rightarrow l-r=4$

Putting the above value in $eq.\left(i\right),$ we get

$\Rightarrow \pi r\times \left(4\right)=88$

$\Rightarrow \frac{22}{7}\times r\times 4=88$

$\Rightarrow r=\frac{88\times 7}{22\times 4}=7cm$

Hence, the radius of the base is $7cm$