Exercise 20G

### A cylindrical water tank of diameter 2.8m and height 4.2m is being fed by a pipe of diameter 7 cm through which water flows at the rate of 4m/s. Calculate, in minutes, the time it takes to fill the tank.

Diameter of cylindrical tank = 2.8 m radius = 1.4 m Height = 4.2 m \[\begin{array}{*{35}{l}} Volume\text{ }of\text{ }water\text{ }filled\text{ }in\text{ }it\text{ }=\text{ }\pi {{r}^{2}}h  \\...

### The cross-section of a tunnel is a square of side 7 m surmounted by a semicircle as shown in the following figure.The tunnel is 80 m long. Calculate:(iii) its floor area

FIGURE: Side of square (a) = 7m the radius of semi-circle = 7/2 m Length of the tunnel = 80 m \[\begin{array}{*{35}{l}} Area\text{ }of\text{ }cross\text{ }section\text{ }of\text{ }the\text{...

### The cross-section of a tunnel is a square of side 7 m surmounted by a semicircle as shown in the following figure.The tunnel is 80 m long. Calculate: (i) its volume (ii) the surface area of the tunnel (excluding the floor)

FIGURE: Side of square (a) = 7m the radius of semi-circle = 7/2 m Length of the tunnel = 80 m \[\begin{array}{*{35}{l}} Area\text{ }of\text{ }cross\text{ }section\text{ }of\text{ }the\text{...

### In the following diagram a rectangular platform with a semicircular end on one side is 22 meters long from one end to the other end. If the length of the half circumference is 11 meters, find the cost of constructing the platform, 1.5 meters high at the rate of Rs 4 per cubic meters.

Length of the platform = 22 m Circumference of semi-circle (c) = 11 m \[\begin{array}{*{35}{l}} radius\text{ }=\text{ }\left( c\text{ x }2 \right)/\text{ }\left( 2\text{ x }\pi  \right)\text{...

### An iron pole consisting of a cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole, given that 1 cm3 of iron has 8 gm of mass (approx). (Take π = 355/113)

Radius of the base of poles (r) = 6 cm Height of the cylindrical part (h1) = 110 cm Height of the conical part (h2) = 9 cm \[\begin{array}{*{35}{l}} Total\text{ }volume\text{ }of\text{ }the\text{...

### Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

Let edge of the cube = a Then, volume of the cube = a x a x a = a3 The sphere that exactly fits in the cube will have radius ‘a/2’ \[\begin{array}{*{35}{l}} Volume\text{ }of\text{ }sphere\text{...

### The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of wire.

Diameter of the sphere = 6 cm Radius = 3 cm \[~volume\text{ }=\text{ }4/3\text{ }\pi {{r}^{3~}}=\text{ }4/3\text{ x }22/7\text{ x }3\text{ x }3\text{ x }3\text{ }=\text{ }792/7\text{...

### A solid is in the form of a cone standing on a hemisphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find in terms of π, the volume of the solid.

Radius of both cone and hemisphere = 8 cm And, height = 8 cm \[\begin{array}{*{35}{l}} Volume\text{ }of\text{ }the\text{ }solid\text{ }=\text{ }Volume\text{ }of\text{ }cone\text{ }+\text{...

### A right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled in identical cones of height 12 cm and diameter 6 cm having a hemi-spherical shape on the top. Find the number of cones required.

Diameter of the cylinder = 12 cm => radius = 6 cm Height of the cylinder = 15 cm Diameter of the cone = 6 cm =>radius = 3 cm Height of the cone = 12 cm Radius of the hemisphere = 3 cm Let the...