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 rectangular room of size 5mX4mX3m is to be painted.If the unit cost of painting is Rs.10 per sq.m, what is the total cost of painting?

Answer:

Explanation:

Area of 4 walls= 2h(l+b)

The area to be painted includes the 4 walls and the top ceiling.

Total area to be painted$=2h(l+b)+lb$ $=2\times 3(5+4)+5\times 4$

$54+20=74 sq.m$

Total cost of painting $=74\times 10=Rs.740$

What is the surface area of the sphere with radius "2r" cm?

Answer:

Explanation:

Surface area of sphere of radius r is $4\pi r^{2}$

When r=2r, Surface area= $4\pi (2r)^{2}=16\pi r^{2}$

Three Spherical balls of radius 1 cm,2 cm and 3 cmmelted to form a single spherical ball.In the process, the material loss was 25%.What would be the radius of the new ball?

Answer:

Explanation:

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

Volume of 3 small spherical balls=$\frac{4}{3} \pi (1^{3}+2^{3}+3^{3}$

                                               =$\frac{4}{3}\pi (1+8+27)$$=\frac{4}{3}\pi \times 36$ $=48\pi$

Material loss =25%

$\therefore$ Volume of the single spherical ball $=\frac{48\pi \times 75}{100}$

$\Rightarrow \frac{48\pi \times 3}{4}= 36\pi$

$=\frac{4}{3}\pi r^{3}=36\pi$ 

$\Rightarrow r^{3}=\frac{36\times 3}{4}=27$ $r=3 cm$

The radius at the base of a conical tent is 7 meters.If the slant height of the tent is 15 meters, what is the area of the canvas required to make the tent?

Answer:

Explanation:

r=7 ms

l=15 m

Area of canvas required = C>S>A of cone =$\pi rl=\frac{22}{7}\times 7\times 15$$=300 sq.m$

A rectangle sheet of size 88 cmX35 cm is bent to form a cylindrical shape with height 35 cm.What is the area of the base of the cylindrical shape?

Answer:

Explanation:

The circumference of the circular region = 88 cm

$2\pi r=88$ $\Rightarrow r=88\times \frac{1}{2}\times \frac{7}{22}$ $=14 cm$

Area of the base $=\pi r^{2}$ $=\frac{22}{7}\times 14\times 14$ $=616 cm^{2}$ 

• Volume and Surface Areas - Volume and Surface Areas I