Question
A solid metal cone with base radius $12\ cm$ and height $24\ cm$ is melted to form solid spherical balls of diameter $6\ cm$ each. Find the number of balls formed.
✓
Answer
Radius of cone $= 12\ cm$
Height of cone $= 24\ cm$
Volume of the metallic cone $=\frac{1}{3}\pi\text{r}^2\text{h}$
$=\frac{1}{3}\pi\times(12)^2\times24$
Radius of spherical ball $=\frac{6}{2}\text{cm}=3\text{cm}$
Volume of each spherical ball $=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\pi\times(3)^3$
Number of balls formed $=\frac{\text{Volume of the metallic cone}}{\text{Volume of each spherical ball}}$
$=\frac{\pi\times12\times12\times24\times3}{3\times4\times\pi\times3\times3\times3}$
$=32$
Height of cone $= 24\ cm$
Volume of the metallic cone $=\frac{1}{3}\pi\text{r}^2\text{h}$
$=\frac{1}{3}\pi\times(12)^2\times24$
Radius of spherical ball $=\frac{6}{2}\text{cm}=3\text{cm}$
Volume of each spherical ball $=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\pi\times(3)^3$
Number of balls formed $=\frac{\text{Volume of the metallic cone}}{\text{Volume of each spherical ball}}$
$=\frac{\pi\times12\times12\times24\times3}{3\times4\times\pi\times3\times3\times3}$
$=32$
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
A number is selected at random from first $50$ natural numbers. Find the probability that it is a multiple of $3$ and $4.$
→Find a quadratic polynomial, the sum and product of whose zeroes are $\sqrt { 2 } , \frac { 1 } { 3 }$ respectively.
→In the figure, $ABC$ and $AMP$ are two right triangles, right angled at $B$ and $M$ respectively. Prove that:
$\triangle ABC \sim \triangle AMP$
$\frac{{CA}}{{PA}} = \frac{{BC}}{{MP}}$
→$\triangle ABC \sim \triangle AMP$
$\frac{{CA}}{{PA}} = \frac{{BC}}{{MP}}$
If $P(2, 6)$ is the mid-point of the line segment joining $A(6, 5)$ and $B(4, y),$ find $y.$
→The following are quadratic equations in $x?$
$\text{x}-\frac{6}{\text{x}}=3$
→$\text{x}-\frac{6}{\text{x}}=3$
Express the following in terms of trigonometric ratios of angles lying between $0^\circ $ and $45^\circ .$
$\cos78^\circ+\sec78^\circ$
→$\cos78^\circ+\sec78^\circ$
Express the following in terms of trigonometric ratios of angles lying between $0^\circ $ and $45^\circ .$
$\sec76^\circ+\text{cosec }52^\circ$
→$\sec76^\circ+\text{cosec }52^\circ$
In the figure given below, a line segment is drawn parallel to one side of the triangle and the lengths of certain line-segment are marked. Find the value of $x$ in the following:
→A die is thrown twice. What is the probability that:
→- $5$ will not come up either time?
- $5$ will come up at least once?
Find the discriminant of the following equation:
$\sqrt3\text{x}^2+2\sqrt2\text{x}-2\sqrt3=0$
→$\sqrt3\text{x}^2+2\sqrt2\text{x}-2\sqrt3=0$