Question
A solid metallic hemisphere of radius 8cm is melted and recasted into a right circular cone of base radius 6cm. Determine the height of the cone.
✓
Answer
As the hemisphere is recasted into a cone. So,Volume of cone = Volume of hemisphere
$\Rightarrow\ \ \frac{1}{3}\pi\text{r}^2\text{h}=\frac{2}{3}\pi\text{R}^3$
$\Rightarrow\ \ \text{r}^2\text{h}=2\text{R}^3$
$\Rightarrow\ \ \text{h}=\frac{2\text{R}^3}{\text{r}^2}=\frac{2\times8\times8\times8}{6\times6}=\frac{32\times8}{9}$
$=\frac{256}{9}=\frac{28.44}{}\text{cm}$
$\Rightarrow\ \ \text{h}=28.44\text{cm}.$
Hence, the height of the cone is 28.44cm.
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
If $\tan\theta=\frac{12}{5},$ find the value of $\frac{1+\sin\theta}{1-\sin\theta}$.
→If $\triangle\text{ABC}$ and $\triangle\text{DEF}$ are two triangles such that $\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{CA}}{\text{FD}}=\frac{3}{4},$ then write $\text{Area}(\triangle\text{ABC}):\text{Area}(\triangle\text{DEF.})$
→Find the mean of the following data using assumed mean method:
| Class: | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 |
| Frequency: | 8 | 7 | 10 | 13 | 12 |
The horizontal distance between two poles is $15 m .$ The angle of depression of the top of first pole as seen from the top of second pole is $30^{\circ}$. If the height of the second pole is $24 ,$ find the height of the first pole. $[\sqrt{3}=1.732]$
→Find the values of k for which the quadratic equation $(3k + 1)x^2 + 2(k + 1)x + 1 = 0$ has real and equal roots.
→Prove that $(\operatorname{cosec} \theta-\cot \theta)^2=\frac{1-\cos \theta}{1+\cos \theta}$.
→Solve for x and y:
x + y = 3,
4x - 3y = 26
x + y = 3,
4x - 3y = 26
Prove that the area of equilateral triangle described on one side of the square is equal to half of the area of an equilateral triangle described on one of its diagonal.
Water is flowing at the rate of 2.52km/h through a cylindrical pipe into a cylindrical tank, the radius of the base is 40cm. If the increase in the level of water in the tank, in half an hour is 3.15m, find the internal diameter of the pipe.
A cone of height $24 \ cm$ and radius of base $6 \ cm$ is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.
→