(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...
Question 1 Report
(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 \(\pi = \frac{22}{7}\)].
Answer Details
(a) Work "of" and \(\div\) before subtraction:
\[\tfrac{5}{8}\text{ of }2\tfrac{1}{2} = \tfrac{5}{8}\times\tfrac{5}{2} = \tfrac{25}{16},\qquad \tfrac{3}{4}\div\tfrac{3}{5} = \tfrac{3}{4}\times\tfrac{5}{3} = \tfrac{5}{4} = \tfrac{20}{16}.\]
\[\tfrac{25}{16} - \tfrac{20}{16} = \tfrac{5}{16}.\]
(b) The cone and the pyramid have equal heights \(h\) and equal volumes.
\[V_{\text{cone}} = \tfrac{1}{3}\pi r^2 h,\qquad V_{\text{pyramid}} = \tfrac{1}{3}(\text{base area})h.\]
Since the volumes and heights are equal, the base areas are equal:
\[\pi r^2 = 154 \Rightarrow \tfrac{22}{7}r^2 = 154 \Rightarrow r^2 = 154\times\tfrac{7}{22} = 49.\]
\[r = 7\text{ cm}.\]
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