Download App

Surface Areas and Volumes — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsSurface Areas and Volumes3 Marks
Question
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
✓

Answer

Let the radius of the hemisphere be r units.
Volume of a hemisphere = Surface area of the hemisphere
$\Rightarrow\frac{2}{3}\pi\text{r}^3=3\pi\text{r}^2$
$\Rightarrow\frac{2}{3}\text{r}=3$
$\Rightarrow\text{r}=\frac{9}{2}$
$\Rightarrow\text{d}=9\text{units}$
Hence, diameter of the hemisphere is equal to 9 units.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Surface Areas and Volumes→Surface Areas and Volumes — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Solve for x and y:
2x - 3y = 13,
7x - 2y = 20
→
A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is $108\ cm$ and the diameter of the cylinder is $36\ cm$, find the cost of polishing the surface at the rate of $7$ paise per $cm^2$. $ (\text{Use}\ \pi=3.1416)$
→
In a cylindrical vessel of diameter $24\ cm$, filled up with sufficient quantity of water, a solid spherical ball of radius 6cm is completely immersed. Find the increase in height of water level.
→
What is the ratio of the volume of a cube to that of a sphere which will fit inside it?
→
Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:
$-3x + 5y = 7$ and $2px - 3y = 1,$
if the lines represented by these equations are intersecting at a unique point.
→
Heights of 50 students of class X of a school are recorded and following data is obtained:
Height (in cm):130-135135-140140-145145-150150-155155-160
Number of Students:411127106

Find the median height of the students.
→
The angle of elevation of the top of the building from the foot of the tower is 30° and the angle of the top of the tower from the foot of the building is 60°. If the tower is 50m high, find the height of the building.
→
Five cards the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards. One card is then picked up at random.
  1. What is the probability that the drawn card is the queen?
  2. If the queen is drawn and put aside and a second card is drawn, find the probability that the second card is: (i) An ace. (ii) A queen.
→
Three circles each of radius 3.5cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.
→
Prove that $2-3\sqrt{5}$ is an irrational number.
→