Question

A girl fills a cylindrical bucket 32 cm in height and 18 cm in radius with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24 cm, find:
(i) its radius and
(ii) Its slant height. (Leave your answer in square root form) [4 MARKS]

Answer 1

Each part: 2 Marks

(i) According to questions,
Volume of cylindrical = Volume of conical heap
$\begin{array}{cc}\Rightarrow & \pi r_1^2{h}_1=\frac{1}{3}\pi r_2^2{h}_2\\ \Rightarrow & 18\times 18\times 32=\frac{1}{3}\times r_2^2\times 24\\ \Rightarrow & r_2^2=18\times 18\times 4\\ \Rightarrow & r^2=36cm\end{array}$
$\therefore$ Radius of the iconical heap = 36 cm

(ii) Now, slant height of conical heap,
$(Use\pi =\frac{22}{7})Numberofcones=\frac{Volumeoficecreamincylinder}{Volumeofcone+Volumeofhemisphere}l=\sqrt{r_2^2+h_2^2}=\sqrt{(36{)}^2+(24{)}^2}=\sqrt{1296+576}=\sqrt{1872}=12\sqrt{13}cm$