Volume of Combined Figures

Q.

A conical tank has height $\text{3 m}$ and radius $\text{2 m}$ at the top.

Water flows in at a rate of ${\text{2 m}}^3{\text{min}}^{-1}$.

How fast is the water level rising when it is $\text{2 m}$?

Q.

__________ times the volume of a cone is equal to the volume of a cylinder having height and radius same as that of the cone.

Q.

Question 9
An ice cream cone full of ice cream having radius 5 cm and height 10 cm as shown in figure. Calculate the volume of ice- cream, provided that its $\frac{1}{6}$part is left unfilled with ice – cream.

Q.

A conical pit of top diameter 3.5 m is 12 m deep.What is its capacity in kilolitres?

Q.

You want to make and sell three different sizes of cylindrical candles. You buy 1 cubic foot of candle wax for $20 to make 8 candles of each size.

a. Design the candles . What are the dimensions of each size of candle ?

Q.

A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy. [4 MARKS]

Q.

A solid consisting of a right circular cone, standing on a hemisphere, is placed upright, in a right circular cylinder, full of water, and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest $c{m}^3$ (Take $\pi =\frac{22}{7}$)

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Q. The volume of a sphere of diameter $d$ is:

1. $\frac{\pi d^3}{3}$
2. $\frac{\pi d^3}{6}$
3. $\frac{2\pi d^3}{3}$
4. $\frac{\pi d^3}{4}$

Q. A shopkeeper has one spherical laddoo of radius $5$ cm. With the same amount of material, how many laddoos of radius $2.5$ cm can be made?

Q.

A field is 80 m long and 50 m broad. In one corner of the field a pit which is 10 m long, 7.5 m broad and 8 m deep has been dug out. The earth taken out of it is evenly spread over the remaining part of the field. If the rise in the level of the field is x(in cm), then x-0.3 =

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