Mensuration Ques 41
Question
Some number of solid metallic right circular cones, radius of which is equal to the side of the square whose area is $9 cm^{2}$ and height is $100 \%$ more than the inradius of that square are melted to form a solid sphere of radius $6 cm$. find the number of right circular cones required.
(1) 64
(2) 36
(3) 27
(4) 32
(5) Other than those given as options
(IBPS Bank PO/MT CWE (Prelim Exam) 12.10.2019)
Show Answer
Correct Answer: (4)
Solution: (4)
Side of square $=\sqrt{9}$ $=3 cm .=$ radius of cone
Height of cone $=2 \times \frac{3}{2}$ $=3 cm$.
Let number of cones be $n$.
$\therefore n \times$ volume of a cone $=$ Volume of sphere
$\Rightarrow n \times \frac{1}{3} \pi \times 3 \times 3 \times 3$ $=\frac{4}{3} \pi \times 6 \times 6 \times 6$
$\Rightarrow n=\frac{4 \times 6 \times 6 \times 6}{3 \times 3 \times 3}=32$
BETA
