Question : The volume of a cone with a height equal to the radius and slant height of 5 cm is:

Option 1: $\frac{125 \pi}{12 \sqrt{3}} \mathrm{~cm}^3$

Option 2: $\frac{125 \pi}{6 \sqrt{3}} \mathrm{~cm}^3$

Option 3: $\frac{125 \pi}{12 \sqrt{2}} \mathrm{~cm}^3$

Option 4: $\frac{125 \pi}{6 \sqrt{2}} \mathrm{~cm}^3$

Question : The ratio of the height and the diameter of a right circular cone is 6: 5 and its volume is $\frac{2200}{7} \mathrm{~cm}^3$. What is its slant height?
(Take $\pi=\frac{22}{7}$ )

Option 1: 26 cm

Option 2: 13 cm

Option 3: 25 cm

Option 4: 5 cm

Question : If the curved surface area of a cylinder is $126\pi$ cm² and its height is 14 cm, what is the volume of the cylinder?

Option 1: $283 \frac{1}{2} \pi\ \mathrm{cm}^3$

Option 2: $137\frac{1}{2} \pi\ \mathrm{cm}^3$

Option 3: $128\frac{1}{2} \pi\ \mathrm{cm}^3$

Option 4: $125\frac{1}{2} \pi\ \mathrm{cm}^3$

Question : The slant height and radius of a right circular cone are in the ratio 29 : 20. If its volume is $4838.4 \pi ~\mathrm{cm}^3$, then its radius is:

Option 1: 28 cm

Option 2: 20 cm

Option 3: 25 cm

Option 4: 24 cm

Question : The area of a sector of a circle is 88 sq. cm., and the angle of the sector is 45°. Find the radius of the circle. (Use $\pi=\frac{22}{7}$)

Option 1: $3 \sqrt{ 11} \mathrm{~cm}$

Option 2: $4 \sqrt{ 14} \mathrm{~cm}$

Option 3: $6 \sqrt{ 13} \mathrm{~cm}$

Option 4: $5 \sqrt{ 14} \mathrm{~cm}$

Question : In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other at X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of the chord PQ is:

Option 1: $2\sqrt{13}\;\mathrm{cm}$

Option 2: $5\sqrt{3}\;\mathrm{cm}$

Option 3: $4\sqrt{6}\;\mathrm{cm}$ 

Option 4: $6\sqrt{5}\;\mathrm{cm}$