6
Q:

# A rectangular block has the dimensions 5x6x7 cm it is dropped into a cylindrical vessel of radius 6cm and height 10 cm. If the level of the fluid in the cylinder rises by 4 cm, What portion of the block is immersed in the fluid ?

 A) 22/7 x 24/35 B) 22/7 x 36 x 4 C) 22/7 x 36/5 D) 22/7 x 37/21

Explanation:

Since level of water increased in cylinder by height 4.

This is because of the rectangular block .

Therefore , area of rectangular block immersed in water is

= $\frac{22}{7}×6×6×4$

Thats why portion of block immersed in water is

= (22/7 * 36 * 4) / total vol. of rectangle

= (22/7 * 36 * 4)/ (7*5*6)

= (22/7 * 24)/ 35.

Q:

The circumference of a circular base of Cylinder is 44 cm and its hight is 15 cm. Then the volume of the cylinder is?

 A) 2759 cub. cm B) 2247 cub. cm C) 2614 cub. cm D) 2311 cub. cm

Explanation:

Given Circumference of a circular base of a cylinder = 44 cm

We know that Circumference of a circle =

Now given the height of a cylinder h = 15 cm

4 201
Q:

What is the Formula for Volume?

The formula to find the volume is given by just multiplying Length, Breadth and Height of that object.

Thus, V = L x B X H

Volume Formulae :

1. Volume of Cube of side 's' = s x s x s = ${\mathbit{s}}^{\mathbf{3}}$  cubic units.

2. Volume of Cylinder${\mathbf{\pi R}}^{\mathbf{2}}\mathbf{h}$ cubic units.

[Where is Radius and h is height]

389
Q:

If radius and height of a cylinder increase by 20% and15% respectively. then what is the % change in curved surface area?

 A) 41% B) 38% C) 33% D) 44%

Explanation:

% Change in Curved Surface Area is given by

8 462
Q:

A town has a population of 4000 requires 140 liters of water per head. It has a tank measuring 18m x 12m x 8m. The water of this tank will suffice for ____ days?

 A) 3 B) 4 C) 5 D) 2

Explanation:

Water required = 4000 x 140 = 560000 lit = 560 cu.m (1 cu.m = 1000 lit)

Volume of tank = 18 x 12 x 8 = 1728 cu.m

Water of this tank will suffice for = 1728/560 = 3 days.

23 792
Q:

A Conical tent was erected by the army at a base camp with height 3 m and base diameter 10 m. If every person requires 3.92 cu.m air, then how many persons can be seated in that tent approximately?

 A) 20 B) 19 C) 17 D) 22

Explanation:

Given height of the conical tent = 3 m

Diameter = 10 => Radius = D/2 = 10/2 = 5 m

Now, as the tent is in the conical form

Volume of the conical tent = $\mathbit{\pi }{\mathbit{r}}^{\mathbf{2}}\frac{\mathbf{h}}{\mathbf{3}}$

=> (22 x 5 x 5 x 3) / (7 x 3)

= 22 x 25/7

= 78.54 cu.m

Given each person requires 3.92 cu.m of air

=> Number of persons can be seated in the tent = 78.54/3.92 = 20.03 =~ 20

15 685
Q:

Ratio between heights of two cylinder in the ratio 3:5. Their volumes are in the ratio 27:80. Find ratio between their radius ?

 A) 1:3 B) 2:1 C) 3:4 D) 4:7

Explanation:

9 726
Q:

The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles  ?

 A) 2413 sq.m B) 1234 sq.m C) 4312 sq.m D) 2143 sq.m

Explanation:

Let the radii of the smaller and the larger circles be 's' m and 'l' m respectively.

$2\mathrm{\pi s}$ = 264 and $2\mathrm{\pi l}$ = 352

s = $\frac{264}{2\mathrm{\pi }}$ and l = $\frac{352}{2\mathrm{\pi }}$

Difference between the areas =$\pi {l}^{2}-\pi {s}^{2}$

= $\mathrm{\pi }\left(\frac{{176}^{2}}{{\mathrm{\pi }}^{2}}-\frac{{132}^{2}}{{\mathrm{\pi }}^{2}}\right)$

= $\frac{1762}{\mathrm{\pi }}-\frac{1322}{\mathrm{\pi }}$

= (176 - 132)(176 + 132) / $\mathrm{\pi }$

= (44 x 308) / (22/7) = 4312 sq.m

9 1502
Q:

If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in sq.cm) is ?

 A) 100 π B) 101/π C) 99 π/12 D) 54/13π