MCQ
A hollow metallic sphere with external diameter 8cm and internal diameter 4cm is melted and moulded into a cone of base radius 8cm. The height of the cone is:
- A12cm
- ✓14cm
- C15cm
- D18cm
✓
Answer
Correct option: B.
14cm
The radii of the spherical shell is 2cm and 4cm.
Volume of the spherical shell $=\frac{4}{3}\pi(\text{R}^3-\text{r}^3)$
$=\frac{4}{3}\pi(4^3-2^3)$
$=\frac{4}{3}\pi(56)$
Radius of the cone = 4cm
Volume of the cone $=\frac{1}{3}\pi\text{r}^2\text{h}$
$=\frac{1}{3}\pi(4)^2\text{h}$
$\therefore\frac{1}{3}\pi(4)^2\text{h}=\frac{4}{3}\pi(56)$
$\Rightarrow16\text{h}=4(56)$
$\Rightarrow\text{h}=14\text{cm}$
Volume of the spherical shell $=\frac{4}{3}\pi(\text{R}^3-\text{r}^3)$
$=\frac{4}{3}\pi(4^3-2^3)$
$=\frac{4}{3}\pi(56)$
Radius of the cone = 4cm
Volume of the cone $=\frac{1}{3}\pi\text{r}^2\text{h}$
$=\frac{1}{3}\pi(4)^2\text{h}$
$\therefore\frac{1}{3}\pi(4)^2\text{h}=\frac{4}{3}\pi(56)$
$\Rightarrow16\text{h}=4(56)$
$\Rightarrow\text{h}=14\text{cm}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Choose the correct answer from the given four options : In two line segments $AC$ and $BD$ intersect each other at the point $P$ such that $PA = 6\ cm, PB = 3\ cm, PC = 2.5\ cm, PD = 5\ cm, \angle\text{APB}=50^\circ$ and $ \ \angle\text{CDP}=30^\circ.$ Then $\angle\text{PBA}$ is equal to :
→The total surface area of a hemisphere of radius $7\ cm$ is :
→$(1+\tan\theta+\sec\theta)(1+\cot\theta-\text{cosec }\theta)=$
→If the sum of two zeroes of the polynomial $x^3-2 x^2+q x-r$ is zero, then
→A tangent $PQ$ at point of contact $P$ to a circle of radius $12\ cm$ meets the line through centre $O$ to a point $Q$ such that $OQ = 20\ cm,$ length of tangent $PQ$ is :
→What is the probability that a leap year has 52 Mondays?
x = ABCDEFGHIJ ... Z. A letter is selected at random from the letters in odd positions. The probability that it is a vowel, is
Three coins are tossed simultaneously, what is the probability of getting at most one tail?
If $A$ is an acute angle of a $\triangle A B C$, right angled at $B$, then the value of $\sin A+\cos A$ is
→The area of the triangle formed by $(a, b + c), (b, c + a)$ and $(c, a + b)$ is:
→