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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?

We have,

Width of the canal = 5.4 m,

Depth of the canal = 1.8 m

It is given that the water is flowing with a speed of 25 km $/$ hr.

Therefore,

Length of the water column formed in 40 mins

That is, $\frac{40}{60} hours = \frac{2}{3} hours$

is $\frac{2}{3} (25) km = \frac{50}{3} km = \frac{50 x 1000}{3} m = \frac{50000}{3} m$

$∴ Volume of the water flowing in \frac{2}{3} hours = Volume of the cuboid of length \frac{50000}{3} m, width 5.4 m and depth 1.8 m \Rightarrow Volume of the water flowing in \frac{2}{3} hours = \frac{50000}{3} x 5.4 x 1.8 = 162000 m^{3}$

This volume = volume of cuboid ( 10 cm of standing water is required for irrigation.)

This volume = base area of field x 0.1 m

$Base area = \frac{162000}{0.1}$

Hence, the cannal irrigates 1620000 m² area in 40 mins.

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.

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