Question

Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of its two circular faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm (see Fig.). If each $c{m}^3$ of molasses has a mass of about 1.2 g, find the mass of the molasses that can be poured into each mould( in kg). (Take $\pi$ = $\frac{22}{7}$)

• A. 10
• B. 12
• C. 14
• D. 16

Answer 1

The correct option is C

14

Since the mould is in the shape of a frustum of a cone, the quantity (volume) of
molasses that can be poured into it = $\frac{\pi }{3}h({r_1}^2+{r_2}^2+r_1{r}_2)$,
where $r_1$ is the radius of the larger base and $r_2$, is the radius of the smaller base.
= $\frac{1}{3}\times \frac{22}{7}\times 14[{\left(\frac{35}{2}\right)}^2+{\left(\frac{30}{2}\right)}^2+(\frac{35}{2}\times \frac{30}{2})]c{m}^3=11641.7c{m}^3$
It is given that 1 $c{m}^3$ of molasses has a mass of 1.2g. So. the mass of the molasses that can be poured into each mould = $(11641.7\times 1.2)g=13970.04g=13.97kg=14kg(approx.)$