A toy is made in the shape of a hemisphere of diameter 7 cm surmounted by a cone. If this 15.5 cm high toy is polished at 20 paise per cm2, then find the cost of polishing. (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ₹42.90
Only the outer surface of the toy is polished: the curved surface of the cone and the curved surface of the hemisphere. The flat circle where they meet is hidden inside the toy.
The cone (its radius is the hemisphere’s, its height the rest of the toy):
Radius of the hemisphere and of the cone: \(r=\frac{7}{2}=3.5\) cm
Height of the cone (the toy less the hemisphere): \(h=15.5-3.5=12\) cm
Slant height \(l=\sqrt{12^2+3.5^2}=\sqrt{156.25}=12.5\) cm
The surface to be polished:
Curved surface of the cone \(\displaystyle =\pi rl=\frac{22}{7}\times3.5\times12.5=137.5\,\mathrm{cm^2}\)
Curved surface of the hemisphere \(\displaystyle =2\pi r^2=2\times\frac{22}{7}\times3.5\times3.5=77\,\mathrm{cm^2}\)
Total surface to be polished \(=137.5+77=214.5\,\mathrm{cm^2}\)
Cost at 20 paise per cm2 \(=214.5\times0.20=\) ₹42.90