Theory question 103
Fractions, Decimals and Approximation(a) Simplify 5/8 of 2 1/2 − 3/4 ÷ 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 cm2, find the base radius of the cone (Take π = 22/7)
Show the model answer
Model answer
(a) 5/8 × 5/2 = 25/16 and 3/4 ÷ 3/5 = 5/4 = 20/16. 25/16 − 20/16 = 5/16.
(b) ⅓πr2h = ⅓ × 154 × h, so πr2 = 154.
r2 = 154 × 7/22 = 49, r = 7 cm.
Explanation
Equal heights and volumes mean the base areas are equal.