Volume of a frustum

Q.

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 $\pi$ = $\frac{22}{7}$)

1. 10

2. 12

3. 16

4. 14

Q.

A container, open from the top and made of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost (in rupees) of the milk which can completely fill the container, at the rate of ₹ 20 per litre.

Also, find the cost (in rupees) of metal sheet used to make the container, if it costs ₹ 8 per 100$c{m}^2$. (Take $\pi$ = 3.14).

1. 221; 156.75

2. 209; 156.75

3. 209; 162.5

4. 221; 162.5

Q.

A frustum of height 14 cm and radii 3 cm and 9 cm is filled with water upto the brim. Find the quantity of water in the frustum.

1. $1716c{m}^3$
2. $5148c{m}^3$
3. $1700c{m}^3$
4. $572c{m}^3$

Q.

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass(in $c{m}^3$).

1. $\frac{308}{3}$

2. $\frac{316}{3}$

3. $\frac{301}{3}$

4. $\frac{320}{3}$

Q.

A bucket made up of metal sheet is in the form of a frustum of a cone. Its depth is $24cm$ and the diameters of the top and bottom are $30cm$ and $10cm$ respectively. Find the cost of milk which can completely fill the bucket at the rate of$Rs20$ per litre and the cost of the metal sheet used, if it costs$Rs10$ per $100c{m}^2$ (use $\mathrm{\pi }=3.14$ )

Q.

A clown’s cap is in the shape of a cone of height 8cm and diameter 12cm. A cut is made from the apex of the cone such that slant height of the newly formed cone is 5cm. Find the ratio of volume of the frustum of the cone formed due to the cut to the volume of the cap.

1. 0.35

2. 0.875

3. 0.3

4. 0.325

Q.

A bucket is in the form of a frustum of a cone, its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. Find how many litres of water can the bucket hold ? (Take $\pi$ = $\frac{22}{7}$)

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Q.

A container made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container at the rate of Rs. 15 per litre and the cost of the metal sheet used, if it costs Rs. 5 per 100 $c{m}^2$. (Take $\pi$= 3·14)

1. 100

2. 97.97

3. 95.63

4. 92.45

Q.

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameter of its two circular ends are 4 cm and 2 cm. The capacity of the glass is $102\frac{2}{3}c{m}^3$.

1. 

2.