(a) Simplify : (frac{5}{8} of 2frac{1}{2} – frac{3}{4} div frac{3}{5}).
(b) A cone and a right pyramid have equal heights and volumes. If the area of the base of the pyramid is (154 cm^{2}), find the base radius of the cone. [Take (pi = frac{22}{7})].
Explanation
(a) (frac{5}{8} of 2frac{1}{2} – frac{3}{4} div frac{3}{5})
= ((frac{5}{8} times frac{5}{2}) – (frac{3}{4} div frac{3}{5}))
= ((frac{25}{16}) – (frac{5}{4}))
= (frac{25 – 20}{16})
= (frac{5}{16})
(b)
(V = frac{1}{3} times A times h = frac{1}{3} pi r^{2} h)
(therefore frac{1}{3} times 154 times h = frac{1}{3} times pi times r^{2} times h)
Comparing the two equations,
(154 = frac{22}{7} times r^{2})
(r^{2} = frac{154 times 7}{22})
(r^{2} = 49)
(therefore r = 7 cm).