Home » Mathematics Theory   The solid is a cylinder surmounted by a hemispherical bowl. Calculate its (a) total…

Mathematics Theory   The solid is a cylinder surmounted by a hemispherical bowl. Calculate its (a) total…

  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}).