The solid is a cylinder surmounted by a hemispherical bowl. Calculate its (a) total surface...
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The solid is a cylinder surmounted by a hemispherical bowl. Calculate its
(a) total surface area ;
(b) volume (Take \(\pi = \frac{22}{7}\))
Explanation
(a) Area of curved surface of cylinder = \(2\pi r h\)
= \(2 \times \frac{22}{7} \times 7 \times 10cm^{2} = 440 cm^{2}\)
Area of the base of cylinder = \(\pi r^{2}\)
= \(\frac{22}{7} \times 7 \times 7 = 154 cm^{2}\)
Surface area of hemisphere = \(\frac{4\pi r^{2}}{2} = 2 \pi r^{2}\)
= \(2 \times \frac{22}{7} \times 7 \times 7 = 308 cm^{2}\)
\(\therefore\) Total surface area = 440 + 154 + 308 = 902cm\(^{2}\)
(b) Volume of cylinder = \(\pi r^{2} h\)
= \(\frac{22}{7} \times 7 \times 7 \times 10 = 1540 cm^{3}\)
Volume of hemisphere = \(\frac{1}{2}(\frac{4\pi r^{3}}{3})\)
= \(\frac{4 \times 22 \times 7 \times 7 \times 7}{2 \times 7 \times 3}\)
= \(718.67 cm^{3}\)
Total volume = 1540 + 718.67 = 2258.67 cm\(^{3}\).