Theory question 103
Mensuration of SolidsThe diagram shows a wooden structure in the form of a cone, mounted on a hemispherical base. The vertical height of the cone is 24cm and the base radius 7cm. Calculate, correct to three significant figures, the surface area of the structure (Take π = 22/7)
Show the model answer
Model answer
Slant height l = √(242 + 72) = √625 = 25 cm.
Curved surface of cone = πrl = 22/7 × 7 × 25 = 550 cm².
Curved surface of hemisphere = 2πr2 = 2 × 22/7 × 49 = 308 cm².
Total surface area = 550 + 308 = 858 cm² (3 s.f.).
Explanation
Only the curved surfaces are on the outside; the flat circle is hidden where the cone meets the hemisphere.