Volume of a Cone

Q. Find the volume of a cone given in the figure.

1. $15\pi {\text{cm}}^3$
2. $16\pi {\text{cm}}^3$
3. $17\pi {\text{cm}}^3$
4. $18\pi {\text{cm}}^3$

Q. What would be the ratio of the volumes of a cone and a cylinder?

1. $\frac{1}{3}$
2. $\frac{3}{1}$
3. $\frac{1}{1}$
4. $\frac{1}{2}$

Q. Tom wants to make a rocket model of the following dimensions.
Find the volume of this rocket model?

1. $77\pi {\text{cm}}^3$
2. $87\pi {\text{cm}}^3$
3. $97\pi {\text{cm}}^3$
4. $107\pi {\text{cm}}^3$

Q. Conical ice cream has a depth and radius of 6 inches and 1 inch respectively. If this ice cream is to be kept in a cylindrical vessel of the same radius and same height. Will the melted ice cream overflow the cylindrical vessel?

1. Yes
2. No

Q. What is the volume of a cone of height h and radius $\frac{h}{2}$.

1. $\frac{h^3\pi }{6}{\text{unit}}^3$
2. $\frac{h^2\pi }{6}{\text{unit}}^3$
3. $\frac{h^3\pi }{6}\text{unit}$
4. $\frac{h^3\pi }{3}{\text{unit}}^3$

Q. If CSA is $x{\text{m}}^2$, TSA is $y{\text{m}}^2$ and Volume is $z{\text{m}}^3$. What is the value of $x+y+z.$

1. $12\pi +4\sqrt{40}$
2. $12\pi +2\sqrt{40}$
3. $6\pi +4\sqrt{40}$
4. $10\pi +4\sqrt{40}$

Q. Volume of a cone is given as $\frac{1}{3}\pi r^{2}L$ for the cone given below.

1. True
2. False