Question

(a) It is required to make a hollow cone 24 cm high whose base radius is 7 cm. Find the area of the sheet metal required including the base. Also, find the capacity of this cone.

(b) The radius and the slant height of a cone are in the ratio 4 : 7. If its curved surface area is 792 $c{m}^2$, find its radius
$(Use\pi =\frac{22}{7})$ [6 MARKS]

Answer 1

Each part: 3 Marks

(a) $\begin{array}{cc}Given& h=24cm.,r=7cm\\ \therefore & l=\sqrt{r^2+h^2}=\sqrt{7^2+{24}^2}\\ & =\sqrt{49+576}=\sqrt{625}=25cm\\ \therefore & Areaofsheetrequired=\pi r^2+\pi rl\\ & =\pi r(r+1)=\frac{22}{7}\times 7\times (7+25)\\ & =22\times 32=704c{m}^2\\ \therefore & Volumeofcone=\frac{1}{3}\pi r^{2}h\\ & =\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 24=1232c{m}^3\end{array}$


(b) $\begin{array}{cc}Given& r:l=4:7\\ Ifr=rx,thenl=7x& Curvedsurfaceareaofcone=792c{m}^2\\ \Rightarrow & \pi rl=792\\ \Rightarrow & \frac{22}{7}\times 4x\times 7x=792\\ \Rightarrow & x^2=\frac{792}{88}=9\Rightarrow x=3cm\\ \therefore & Radiusofcone,r=4x=4\times 3=12cm\end{array}$