66
(a) A spherical glass vessel has a cylindrical neck $7$ cm long and $8$ cm in diameter. The radius of spherical part is $10$ cm. Find the volume of the vessel.
OR
(b) From each end of a solid cylinder of height $20$ cm and base radius $7$ cm, a cone of base radius $2.1$ cm and height $5$ cm is scooped out. Find the volume of the remaining solid.
OR
(b) From each end of a solid cylinder of height $20$ cm and base radius $7$ cm, a cone of base radius $2.1$ cm and height $5$ cm is scooped out. Find the volume of the remaining solid.
Show SolutionHide Solution↓
Solution: (a) Volume of the vessel $= \frac{4}{3} \times \frac{22}{7} \times 10 \times 10 \times 10 + \frac{22}{7} \times 4 \times 4 \times 7 = 4190.4 + 352 = 4542.48$ cu. cm
OR
(b) Volume of cylinder $= \frac{22}{7} \times 7 \times 7 \times 20 = 3080$ cu. cm
Volume of cones $= 2 \times \frac{1}{3} \times \frac{22}{7} \times \frac{21}{10} \times \frac{21}{10} \times 5 = 46.2$ cu. cm
Volume of remaining solid $= 3080 - 46.2 = 3033.8$ cu. cm
OR
(b) Volume of cylinder $= \frac{22}{7} \times 7 \times 7 \times 20 = 3080$ cu. cm
Volume of cones $= 2 \times \frac{1}{3} \times \frac{22}{7} \times \frac{21}{10} \times \frac{21}{10} \times 5 = 46.2$ cu. cm
Volume of remaining solid $= 3080 - 46.2 = 3033.8$ cu. cm