Volume of a Frustum

Q.

A right cylinder and a right circular cone have the same radius and same volumes.The ratio of the height of the cylinder to that of the cone is

1. 3:5

2. 2:5

3. 3:1

4. 1:3

Q.

If the volume of a right circular cone of height $9cm$ is $48\pi c{m}^3$, find the diameter of its base.

Q.

If the radius of a right circular cone is halved and height is doubled, then the volume will remain unchanged.

Q.

The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former.The ratio of their radii is

1. 1:1

2. 2:1

3. 4:1

4. 8:1

Q.

Find the curved surface area of a cone with base radius $5.25cm$ and slant height $10cm.$

Q.

Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m. $[Assume\pi =\frac{22}{7}]$

Q. Question 3
Curved surface area of a cone is $308c{m}^2$ and its slant height is 14 cm. Find
(i) radius of the base.
(ii) total surface area of the cone. $[Assume\pi =\frac{22}{7}]$

Q.

Question 13
The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm, respectively. The curved surface area of the bucket is

(A) $4950c{m}^2$
(B) $4951c{m}^2$
(C) $4952c{m}^2$
(D) $4953m^2$

Q.

The volume of a right circular cone is $110m^3$ and diameter is $2\sqrt{15}m$. Calculate
i) Height of the cone
ii) Slant height
iii) Curved Surface area [4 MARKS]

Q. A right circular cone is $8\text{cm}$ high, the radius of the base is $6\text{cm}$. Find the curved surface area

1. $314{\text{cm}}^2$
2. $315{\text{cm}}^2$
   
3. $413{\text{cm}}^2$
   
4. $431{\text{cm}}^2$
   

Q.

A conical tomb is made up of bricks of a front surface area of $5m^2$. The slant height and radius of the tomb are measured to be $25m$ and $7m$ respectively. The approximate number of bricks made used to construct the tomb are

[Take $\pi =\frac{22}{7}$]

1. 110

2. 150

3. 160

4. 100

Q.

If the area of a circle with radius r is equal to the curved surface area of a cone with radius $r_1$ and slant height l then the value of $r_1$ in terms of r and l is:

1. = rl

2. None of these

3. =

4. = rl

Q. From a right circular cylinder with height $10cm$ and radius of base $6cm$, a right circular cone of the same height and base is removed. Find the volume of the remaining solid

1. $754.28{cm}^3$
2. $714.17{cm}^3$
3. $754.82{cm}^3$
4. $654.18{cm}^3$

Q. The slant height of a right circular cone is $10\text{m}$ and its height is $8\text{m}$. Find the area of its curved surface.

1. $80\pi {\text{m}}^2$
2. $30\pi {\text{m}}^2$
3. $40\pi {\text{m}}^2$
4. $60\pi {\text{m}}^2$

Q. A vessel in the form of an inverted cone is filled with water to the brim. Its height is $32cm$ and diameter is $25.2cm.$ Two equal solid cones are dropped in it so that they are fully submerged. As a result, one-third of the water in the original cone overflows. What is the volume of each of the solid cone submerged?

Q.

A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio 3:1.

Q. The radius and slant height of a right circular cone are in the ratio of $7:13$ and its curved surface area is ${286cm}^2$.Find its radius $(Use\pi =\frac{22}{7})$.

Q. Find the total surface area of a cone, if its slant height is $21m$ and diameter of its base is $24m$.

1. $1244.57m^2$
2. $1144.57m^2$
3. $2244.57m^2$
4. $1277.57m^2$

Q. A conical vessel of slant height $10$ $m$ and radius $5m$ is being filled with water at a uniform rate of $1.5$ $m^3/min$. How long will it take to fill the vessel?

1. $151$ min
2. $41$ min
3. $59$ min
4. $72$ min

Q. Diameter and slant height of a cone are $14m$ and $25m$ respectively. Find it total surface area.

Q. A heap of rice is in the form of a cone of diameter $9$ m and height $3.5$ m. The volume of the rice is $74.25$ $m^3$. Canvas cloth required to just cover the heap is $80.62$ $m^2$.Write $1$ if true and $0$ if false.

Q. If the volumes of two cones are in the ratio $1:4$ and their diameter are in the ratio $4:5$, then write the ratio of their weights.

Q. Fill in the blanks:
A cone has one ____ face and one _____ face.