Arithmetic aptitude :: Volume and Surface Areas :: Volume and Surface Areas I

• Volume and Surface Areas - Volume and Surface Areas I
• Volume and Surface Areas - Important Formulas and Facts

Introduction:

The term 'Volume' refers to the space occupied by the figures in 'three dimensions'Eg Cube,cuboid,Cone,Cylinder,Sphere etc.

Volume of a combination of solids:

The volume of the solid formed by joining two basic solids will actually be the sum of the volumes of the constituents.

Total Surface Area:

The total surface area of a solid is the sum of the curved surface area + the sum of the area of the smooth surface.

A copper sphere of radius 3 cm is beaten and drawn into wire of diameter 0.2 cm. The length of the wire is

Answer:

Explanation:

Volume of copper sphere =$\frac{4}{3}\pi r^{3}$

=$\frac{4}{3}\pi 3^{3}$

Radius of the wire =0.1 cm

Let h be the lenght of the cylinder 

$\pi r^{2}h=36\pi$

$\pi (0.1)^{2}h=36\pi$

$h=\frac{36}{0.01}=3600 cm$

h=36 m

A semi circular sheet of a paper of diameter 28 cm is bent to cover the exterior surface of an open conical ice cream cup. The length of the ice cream cup is:

Answer:

Explanation:

Radius of the semi circular sheet = height of the cone

Therefore height = $\frac{28}{2}=14 cm$

The circumference of the base of a 10m high conical tent is 44 metres. Calculate the length of canvas used in making the tent , where the width of the canvas is 2m.

Answer:

Explanation:

Let r be the radius of the base,

Given $2\pi r=44$

$2\times \frac{22}{7}\times r=44$

$r=\frac{44\times 7}{2\times 22}=7 m$

Let the slant height = 1 m

$1=\sqrt{h^{2}+r^{2}}$

=$\sqrt{7^{2}+10^{2}}=12.2 m$

Surface Area = $\pi rl= \frac{22}{7}\times 7\times 12.2=268.4m^{2}$

Area canvas = 268.4 $m^{2}$,width=2 m

Lenght of canvas =$\frac{268.4}{2}=134.2 m$

500 men took a dip in a tank which is 80m long and 50m broad. What is the rise in the water level if the average displacement of water by a man is $4m^{3}$.

Answer:

Explanation:

Volume of water displayed by 1 man = $4m^{3}$

Volume of water displayed by 500 men =$4\times 500$

                                                         =$2000m^{3}$

Let xm be the rise in water level in the tank.

Therefore, Volume of water in the tank = $80\times 50\times xm^{3}$

$80\times 50\times x=2000$

x=$\frac{2000}{80\times 50}$

=$\frac{1}{2}m$

= 50 cm

100 persons can sleep in a room 25m by 9.8m.If each person requires 12.25 cu.m of air. Find the height of the room.

Answer:

Explanation:

Let the height of the room be h m.

Then, volume of the room = $25\times 9.8\times h m^{3}$

=$245hm^{3}$

Given, $245h=100\times 12.25$

h=$\frac{1225}{245}$

=5 m

• Volume and Surface Areas - Volume and Surface Areas I