Volume of a Right Circular Cone

Q. Match the following :
$\begin{array}{cc}\text{A. Volume of Cone}& i.\pi r^{2}h\\ \text{B. Volume of Sphere}& ii.\frac{4}{3}\pi r^3\\ \text{C. Volume of Cylinder}& iii.\frac{\left(\pi r^{2}h\right)}{3}\end{array}$

1. A - iii, B - ii, C - i
2. A - ii, B - i, C - iii
3. A - i, B - iii, C - ii
4. A - iii, B - i, C - ii

Q.

The surface area of a solid metallic sphere is $2464c{m}^2$. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate the number of cones recast.

1. 128

2. 64

3. 32

4. 256

Q. A girl fills a cylindrical bucket whose height is 32 cm and radius is 18 cm with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24 cm, then the slant height of the cone formed is:

1. $13\sqrt{12}cm$

2. $12\sqrt{13}cm$

3. $6\sqrt{26}cm$

4. $12\sqrt{7}cm$

Q.

A conical tent is to accommodate 11 persons. Each person must have 4 square metres of the space on the ground and $20m^3$ of air to breathe. Find the height of the cone.

1. 18 m

2. 16 m

3. 15 m

4. 20 m

Q.

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume is $\frac{1}{27}$ of the volume of the given cone, at what height above the base is the section made?

1. 10 cm
2. 20 cm
3. 40 cm
4. 15 cm

Q.

A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of the height of cylinder to cone is 4:3, the ratio of their volume is

1. 2:1

2. 3:1

3. 4:1

4. 1:1

Q.

If the rate of flow of water from a pipe is $2m^3{s}^{-1}$, then how much time will it take to fill a bucket whose volume is $1200m^3$?

1. 8 min

2. 9 min

3. 10 min

4. 12 min

Q.

A right angle triangle of base 4 cm and height 3 cm is rotated about its height. The curved surface area and volume of the solid obtained are _____ ($inc{m}^2$) and _____ ($inc{m}^3$) respectively.

1. $18\pi \&14\pi$
2. $20\pi \&16\pi$
3. $16\pi \&18\pi$
4. $22\pi \&20\pi$

Q.

Pavan built a conical flask using 550$m^2$ of aluminium sheet. If the radius of the flask is 7m, then how much water can he fill into the flask?

1. $1232000l$

2. $1232m^3$

3. $12.32m^3$

4. $123200l$

Q.

The volume of a cone whose height and radius is 6 cm and 5 cm respectively is:

1. 50π

2. 45π

3. 55π

4. 40π