(a) Simplify : \(\frac{5}{8} of 2\frac{1}{2} - \frac{3}{4} \div \frac{3}{5}\).
(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 \(\pi = \frac{22}{7}\)].
(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 \(\pi = \frac{22}{7}\)].
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Correct Answer: Option
Explanation:
(a) \(\frac{5}{8} of 2\frac{1}{2} - \frac{3}{4} \div \frac{3}{5}\)
= \((\frac{5}{8} \times \frac{5}{2}) - (\frac{3}{4} \div \frac{3}{5})\)
= \((\frac{25}{16}) - (\frac{5}{4})\)
= \(\frac{25 - 20}{16}\)
= \(\frac{5}{16}\)
(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,
\(154 = \frac{22}{7} \times r^{2}\)
\(r^{2} = \frac{154 \times 7}{22}\)
\(r^{2} = 49\)
\(\therefore r = 7 cm\).
(a) \(\frac{5}{8} of 2\frac{1}{2} - \frac{3}{4} \div \frac{3}{5}\)
= \((\frac{5}{8} \times \frac{5}{2}) - (\frac{3}{4} \div \frac{3}{5})\)
= \((\frac{25}{16}) - (\frac{5}{4})\)
= \(\frac{25 - 20}{16}\)
= \(\frac{5}{16}\)
(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,
\(154 = \frac{22}{7} \times r^{2}\)
\(r^{2} = \frac{154 \times 7}{22}\)
\(r^{2} = 49\)
\(\therefore r = 7 cm\).