108
(a) A hemispherical bowl of internal diameter $42$ cm contains a liquid. This liquid is to be filled in cylindrical bottles of radius $3$ cm and height $8$ cm. How many bottles are required to empty the bowl ?
OR
(b) A solid is composed of a cylinder with hemispherical ends. If the total height of the solid is $16.2$ cm and the diameter of the cylinder is $4.2$ cm, find the volume and total surface area of solid. [$\pi = \frac{22}{7}$]
OR
(b) A solid is composed of a cylinder with hemispherical ends. If the total height of the solid is $16.2$ cm and the diameter of the cylinder is $4.2$ cm, find the volume and total surface area of solid. [$\pi = \frac{22}{7}$]
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(a) Volume of hemisphere $= \frac{2}{3} \times \pi \times 21 \times 21 \times 21$
Volume of cylinder $= \pi \times 3 \times 3 \times 8$
$\therefore$ Numbers of bottles $= \frac{\text{volume of hemisphere}}{\text{volume of cylinder}} = 85.75$
Hence, $86$ bottles are required to empty the bowl
OR
(b)
$r = 2.1$ cm and $h = 16.2 - 4.2 = 12$ cm
Volume of the solid $= \pi r^2 h + \frac{4}{3} \pi r^3 = \frac{22}{7} \times \frac{21}{10} \times \frac{21}{10} \times 12 + \frac{4}{3} \times \frac{22}{7} \times \frac{21}{10} \times \frac{21}{10} \times \frac{21}{10} = 205.13$ cu.cm
Total surface area of the solid $= 2\pi rh + 4\pi r^2 = 2 \times \frac{22}{7} \times \frac{21}{10} \times 12 + 4 \times \frac{22}{7} \times \frac{21}{10} \times \frac{21}{10} = 213.84$ sq.cm
Volume of cylinder $= \pi \times 3 \times 3 \times 8$
$\therefore$ Numbers of bottles $= \frac{\text{volume of hemisphere}}{\text{volume of cylinder}} = 85.75$
Hence, $86$ bottles are required to empty the bowl
OR
(b)
$r = 2.1$ cm and $h = 16.2 - 4.2 = 12$ cm
Volume of the solid $= \pi r^2 h + \frac{4}{3} \pi r^3 = \frac{22}{7} \times \frac{21}{10} \times \frac{21}{10} \times 12 + \frac{4}{3} \times \frac{22}{7} \times \frac{21}{10} \times \frac{21}{10} \times \frac{21}{10} = 205.13$ cu.cm
Total surface area of the solid $= 2\pi rh + 4\pi r^2 = 2 \times \frac{22}{7} \times \frac{21}{10} \times 12 + 4 \times \frac{22}{7} \times \frac{21}{10} \times \frac{21}{10} = 213.84$ sq.cm