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Surface Areas and Volumes

Short Answer Type

731.

If the total surface area of a solid hemisphere is 462 cm², find its volume.

$[Take π = \frac{22}{7}]$

Long Answer Type

732.

The largest possible sphere is carved out of a wooden solid cube of side 7 cm. Find the volume of the wood left. $[U s e π = \frac{22}{7}]$

733.

Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?

734.

150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.

735.

A container open at the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular ends, as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of 21 per litre.

$[Use π = \frac{22}{7}]$

736.

Water in a canal, 5.4 m wide and 1.8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation?

737.
The dimensions of a solid iron cuboid are 4.4 m × 2.6 m × 1.0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe.

Let the length of the pipe be h cm.

Then, volume of iron pipe = volume of iron in the block.

Volume of the block = ( 4.4 x 2.6 x 1 ) m³ = ( 440 x 260 x 100 ) cm³

r = Internal radius of the pipe = 30 cm

R = External radius of the pipe = ( 30 + 5 ) = 35 cm

$∴$ Volume of the iron pipe = ( External volume ) - ( internal volume )

$= {πR}^{2} h - {πr}^{2} h = π (R^{2} - r^{2}) h = π (R + r) (R - r) h = π (35 + 30) (35 - 30) x h = π x 65 x 5 x h$

Now, volume of iron in the pipe = volume of iron in the block

$\Rightarrow π x 65 x 5 x h = 440 x 260 x 100 \Rightarrow \frac{22}{7} x 65 x 5 x h = 440 x 260 x 100 \Rightarrow h = \frac{440 x 260 x 100 x 7}{22 x 65 x 5} \Rightarrow h = 11200 cm \Rightarrow h = 112 m$

Thus, the length of the pipe is 112 m.

738.

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

739.

In a rain–water harvesting system, the rain-water from a roof of 22 m × 20 m drains into a cylindrical tank having diameter of base 2 m and height 3.5m. If the tank is full, find the rainfall in cm. Write your views on water conservation

Multiple Choice Questions

740.

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

1 : 2
2 : 1
1 : 4
4 : 1