Volume of a Right Circular Cone

Q. Find the volume of the cone if the height and radius is 12 inches and 7 inches, respectively. $(\text{Use}:\pi =\frac{22}{7})$

1. $420{\text{in}}^3$
2. $313{\text{in}}^3$
3. $516{\text{in}}^3$
4. $616{\text{in}}^3$

Q. A village has a population of 4000, requires 150 litres water per head per day. It has a tank measuring 20 m , 15 m , 6 m. How many days for the water is sufficient enough once the tank is made full.

Q.

2 solid cones X and Y are placed in a cylindrical tube as shown below. The ratio of their capacities is 3:1. Find the volume of the remaining portion of the cylinder.

1. $\frac{128}{3}{units}^3$
2. $\frac{108}{3}\pi {units}^3$
3. $\frac{128}{3}\pi {units}^3$
4. $128{units}^3$

Q. A sector of a circle of radius $10$ cm is folded such that it forms into a cone. If the central angle of the sector is ${144}^{{}^{\circ }}$ then what is the volume of the cone formed ? (in $c{m}^3$ )

1. $\frac{704\sqrt{21}}{21}$
2. $\frac{628\sqrt{11}}{11}$
3. $\frac{576\sqrt{21}}{21}$
4. $\frac{682\sqrt{11}}{11}$

Q.

The radius and height of a right circular cone are in the ratio $1:2$. If its volume is $144{cm}^3$, find its slant height.

1. 6 cm

2. 4 cm

3. 5 cm

4. 5 cm

Q. A right angled triangle ABC with sides $5cm$, $12cm$ and $13cm$ is revolved about the side $12cm$. Find the volume of the solid so obtained

1. $314.28c{m}^3$
2. $30.28c{m}^3$
3. $34.28c{m}^3$
4. $14.28c{m}^3$

Q.

Question 112

A rectangular sheet of dimensions $25cm\times 7cm$ is rotated about its longer side. Find the volume and the whole surface area of the solid thus generated.

Q. Milk World Ltd. is a government-owned milk distribution center. Earlier they used to distribute milk in bottles as shown in the figure for Rs. 8 per bottle. Now they have decided to reduce the price per bottle by 50 paise, by reducing the size of the bottle, However, they do not want their old customers to notice this change in the size of the bottle, so they plan to reduce the circumference of the opening of the bottle without changing the height of the bottle. What is the new circumference of the opening?

1. $6\pi cm$
2. $8\pi cm$
3. $3.5\pi cm$
4. Cannot be determined

Q. A tent is in the shape of a right circular cylinder surmounted by cone. The total height and the diameter of the base are $13.5$ m and $28$ m, respectively. If the height of the cylindrical portion is $3$ m, find the total surface area of the tent.

Q. The curved surface area of a cylindrical pillar is 264 sq. m and its volume is 924 cub. m. Find the ratio of its diameter to its height.

1. 3 : 7
2. 7 : 3
3. 6 : 7
4. 7 : 6

Q. Find the total volume of the following figure.

1. $24\pi c{m}^3$
2. $26\pi c{m}^3$
3. $30\pi c{m}^3$
4. $28\pi c{m}^3$

Q. If the volume of the cone is 66 $i{n}^3$ and the diameter is 6 in, then what is the height of the cone? $(\text{use}\pi =\frac{22}{7})$