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 = (2pi 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{4pi 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{4pi 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}).