The 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 height 7cm. Calculate, correct to three significant figures, the surface area of the structure. [Take (pi = frac{22}{7})].
Explanation
Let the slant height = L ; height = 24cm ; r = 7cm.
(therefore L^{2} = 24^{2} + 7^{2} = 576 + 49 = 625)
(L = sqrt{625} = 25cm)
Surface area of the structure = Area of cone + Area of hemisphere
= (pi r L + 2 pi r^{2} = pi r (L + 2r))
= (frac{22}{7} times 7 (25 + 2(7)))
= (22 times 39 = 858 cm^{2})