Theory question 109
Mensuration of SolidsThe solid above is a cylinder surmounted by a hemispherical bowl. Calculate its: (a) total surface area; (b) Volume. (Take π = 22/7).
Show the model answer
Model answer
From the diagram the radius is 7 cm and the cylinder is 10 cm high.
(a) Curved surface of cylinder = 2πrh = 2 × 22/7 × 7 × 10 = 440 cm2.
Hemisphere = 2πr2 = 308 cm2. Base = πr2 = 154 cm2.
Total = 440 + 308 + 154 = 902 cm2.
(b) Volume = ⅔πr3 + πr2h = 718⅔ + 1540 = 2258⅔ ≈ 2258.7 cm3.
Explanation
Add the separate surfaces that are on the outside: cylinder wall, hemisphere and flat base.