Sample QuestionsSurface Areas And Volumes questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is $5\ cm$, then height of the cone is:
- A
$10\ cm$
- ✓
$15\ cm$
- C
$18\ cm$
- D
$24\ cm$
Answer: B.
View full solution →If two solid-hemispheres of same base radius $r$ are joined together along their bases, then curved surface area of this new solid is:
- ✓
$4\pi\text{r}^2$
- B
$6\pi\text{r}^2$
- C
$3\pi\text{r}^2$
- D
$8\pi\text{r}^2$
Answer: A.
View full solution →The diameters of two circular ends of the bucket are $44\ cm$ and $24\ cm$. The height of the bucket is $35\ cm$. The capacity of the bucket is:
- ✓
$32.7$ litres
- B
$33.7$ litres
- C
$34.7$ litres
- D
$31.7$ litres
Answer: A.
View full solution →The maximum volume of a cone that can be carved out of a solid hemisphere of radius $r$ is:
Answer: B.
View full solution →A reservoir is in the shape of a frustum of a right circular cone. It is $8m$ across at the top and 4m across at the bottom. If it is $6m$ deep, then its capacity is:
- ✓
$176 m^3 $
- B
$ 196 m^3 $
- C
$ 200 m^3$
- D
$ 110 m^3$
Answer: A.
View full solution →A cylindrical bucket $28\ cm$ in diameter and $72\ cm$ high is full of water. The water is emptied into a rectangular tank $66\ cm$ long and $28\ cm$ wide. Find the height of the water level in the tank.
View full solution →A rectangular tank $15m$ long and $11m$ broad is required to receive entire liquid contents from a fully cylindrical tank of internal diameter $21m$ and length $5m$. Find the least height of the tank that will serve the purpose.
View full solution →A spherical ball of iron has been melted and made into smaller balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?
$25$ circular plates, each of radius $10.5\ cm$ and thickness $1.6\ cm$, are placed one above the other to form a solid circular cylinder. Find the curved surface area and
the volume of the cylinder so formed.
View full solution →A solid metallic sphere of radius $5.6\ cm$ is melted and solid cones each of radius $2.8\ cm$ and height $3.2\ cm$ are made. Find the number of such cones formed.
View full solution →If the heights of two right circular cones are in the ratio $1 : 2$ and the perimeters of their bases are in the ratio $3 : 4,$ what is the ratio of their volumes$?$
View full solution →A well of diameter $3m$ is dug $14m$ deep. The earth taken out of it has been spread evenly all around it to a width of 4m to form an embankment. Find the height of the embankment.
View full solution →A cylindrical tank full of water is emptied by a pipe at the rate of $225$ litres per minute. How much time will it take to empty half the tank, if the diameter of its base is $3m$ and its height is $3.5m?$
View full solution →What is the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?
The height of a solid cylinder is $15\ cm$ and the diameter of its base is $7\ cm.$ Two equal conical holes each of radius $3\ cm,$ and height $4\ cm$ are cut off. Find the volume of the remaining solid.
View full solution →A tent is of the shape of a right circular cylinder upto a height of $3\ m$ and then becomes a right circular cone with a maximum height of $13.5\ m$ above the ground. Calculate the cost of painting the inner side of the tent at the rate of $Rs. 2$ per square metre, if the radius of the base is $14\ m.$
View full solution →The height of a cone is $20\ cm$. A small cone is cut off from the top by a plane parallel to the base. If its volume be $\frac{1}{125}$ of the volume of the original cone, determine at what height above the base the section is made.
View full solution →A bucket is in the form of a frustum of a cone with a capacity of $12308.8cm^3$ of water. The radii of the top and bottom circular ends are 20cm and 12cm respectively. Find the height of the bucket and the area of the metal sheet used in its making.$(\text{use}\ \pi=3.14)$
View full solution →An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is $\frac{1}{4}$ of the radius of the original ball, how many such balls are made? Compare the surface area, of all the smaller balls combined together with that of the original ball.
View full solution →The radii of the ends of a bucket $30\ cm$ high are $21\ cm$ and $7\ cm$. Find its capacity in litres and the amount of sheet required to make this bucket.
View full solution →