Question

A juiceseller has a large cylindrical vessel of base radius 15 cm filled up to a height of 32 cm with orange juice. The juice is filled in small cylindrical glasses of radius 3 cm up to a height of 8 cm, and sold for ₹ 15 each. How much money does he received by selling the juice completely?

Answer 1

Radius of the vassel, R = 15 cm

Height of orange juice in the vassel, H = 32 cm

∴ Volume of orange juice in the vassel = $\mathrm{\pi }{R}^{2}H=\mathrm{\pi }\times {\left(15\right)}^2\times 32{\mathrm{cm}}^3$

Radius of the glass, r = 3 cm

Height of orange juice in the glass, h = 8 cm

∴ Volume of orange juice in each glass = $\mathrm{\pi }{r}^{2}h=\mathrm{\pi }\times {\left(3\right)}^2\times 8{\mathrm{cm}}^3$

Number of glasses of orange juice sold by the juiceseller

$$\begin{gathered} =\frac{\mathrm{Volume}\mathrm{of}\mathrm{orange}\mathrm{juice}\mathrm{in}\mathrm{the}\mathrm{vassel}}{\mathrm{Volume}\mathrm{of}\mathrm{orange}\mathrm{juice}\mathrm{in}\mathrm{each}\mathrm{glass}} \\ =\frac{\mathrm{\pi }\times {\left(15\right)}^2\times 32}{\mathrm{\pi }\times {\left(3\right)}^2\times 8} \\ =100 \end{gathered}$$
Rate of each glass of orange juice = ₹ 15

∴ Total money received by the juiceseller

= Number of glasses of orange juice sold by the juiceseller × Rate of each glass of orange juice

= 100 × 15

= ₹ 1,500

Thus, the total money received by the juiceseller by selling the juice completely is ₹ 1,500.