In this page we will to solve questions related to mensuration. All the questions are in Multiple choice questions format and have been previously asked in examinations.

Question of mensuration basically involves calculation of dimensions, area and volume of important figures. To solve these questions, you should be aware of the formulas and techniques of important figures.

For every question, we have tried to provide you with step by step solution so that there is no room of doubt left among the students.

## Area and Volume Aptitude Questions

### (01) Find the length of the largest rod that can be placed in a room 16 meter long, 12 meter broad and 32/3 meter high?

a. 123 meter

b. 68 meter

c. 68/3 meter

d. 67/3 meter

The rod is placed in such a way that it touches the opposite sides of the room as given in the below figure. Which means that the length of largest rod is equal to the diagonal of the rectangular room

The formula for the diagonal of rectangular room is given as

Diagonal\quad =\sqrt { { length }^{ 2 }+{ breadth }^{ 2 }+{ height }^{ 2 } }\\\ \\ =\sqrt { { 16 }^{ 2 }+{ 12 }^{ 2 }+({ \frac { 32 }{ 3 } ) }^{ 2 } } \\\ \\ =\sqrt { 256+144+\frac { 1024 }{ 9 } }\\\ \\ =\sqrt { 400+\frac { 1024 }{ 9 } }\\\ \\ =\sqrt { \frac { 3600+1024 }{ 9 } } \\\ \\ =\quad \sqrt { \frac { 4624 }{ 9 } }\\\ \\ =\quad \frac { 68 }{ 3 } =22\frac { 2 }{ 3 } .**Hence (c) is the right answer**

### (02) The perimeter of rectangle is 160 meter and the difference of two sides is 48 meter. Find the side of a square whose area is equal to the area of this rectangle

a. 32 meter

b. 8 meter

c. 4 meter

d. 16 meter

Given,

Perimeter of rectangle = 160 meter

that means,

==> 2* (Length + Breadth) = 160 meter

==> (Length + Breadth) = 80 meter –(1)

Also, its given that

==> Length – Breadth = 48 meter –(2)

On solving equation (1) & (2), we get

Length = 64 meters and Breadth = 16 meters

According to question

==> Area of Square = Area of Rectangle

==> Side * Side = 64 * 16

==> Side = 32 meter

**Option (A) is the right answer**

### (03) A wire when bent in the form of square encloses an area of 484 sq. cm. What will be enclosed area when the wire is bent in the form of circle?

a. 125 sq cm

b. 230 sq cm

c. 550 sq cm

d. 616 sq cm

Read Solution

Area of square = 484 sq cm

Side * Side = 22 * 22

Side of square = 22 cm

Perimeter of square = 4 * Side => 4 * 22 => 88 cm

Circumference of wire = Perimeter of square

2\pi r\quad =88\\\ \\ 2\times \frac { 22 }{ 7 } \times \quad r\quad =88\\\ \\ r\quad =\quad 14\quad cm\\\ \\ \\\ \\ \ area\quad of\quad wire\quad =\quad \pi { r }^{ 2 }\\\\ \\ \qquad \ \qquad \qquad \qquad =\frac { 22 }{ 7 } \times \quad 14\times \quad 14\\\ \\ \ \qquad \qquad \qquad \qquad =\quad 616\quad sq.\quad cm\quad**Option (D) is correct**

### (04) A took 15 seconds to cross a rectangular field diagonally walking at the ratio of 52 meters/min and B took the same time to cross the same field along its sides walking at the rate of 68 meters/min. Find the area of the field?

a. 30 sq m

b. 40 sq m

c. 50 sq m

d. 60 sq m

Read Solution

Distance travelled by A in 15 seconds = (52 * 15) / 60 = 13 meter

Diagonal of the field= 13 meter

Applying Pythagoras Theorem

\sqrt { { l }^{ 2 }+{ b }^{ 2 } } =\quad { 13 }\\\ \\ squaring\quad on\quad both\quad sides,\\\ \\ { l }^{ 2 }+{ b }^{ 2 }\quad =\quad 169

Distanced travelled by B in 15 seconds = (68 * 15)/60 => 17 meter

l+b=17\quad m\\\ \\ { (l+b) }^{ 2 }={ l }^{ 2 }+{ b }^{ 2 }+2\times l\times b\\\ \\ { 17 }^{ 2 }=169+2lb\\\ \\ 289\quad =\quad 169\quad +2lb\\\ \\ 2lb\quad =289-169\ 2lb\quad =120\ lb\quad =\quad 60\quadTherefore area is 60 sq. meter

**Option (D) is the right answer**

### (05) There is a rectangular tank of length 180 meter and breadth 120 meter in a circular field. If the area of the land portion of the field is 40,000 sq meter, what is the radius of the field?

a. 130 m

b. 135 m

c. 140 m

d. 145 m

Read Solution

Length of tank = 180 meter

Breadth of tank = 120 meter

Area of tank = Length * Breadth

==> 180 * 120

==> 21600 sq meter

Area of land portion = 40,000 sq. m

Area of circular field = Area of tank + Area of land portion

==> 21600 + 40000 => 61600 sq m

Let r be the radius of circular field

Area\quad of\quad field\quad =\quad \pi { r }^{ 2 }\\\ \\ \quad \quad 61600\qquad \quad =\quad \frac { 22 }{ 7 } \times \quad r^{ 2 }\ r^{ 2 }\\\ \\quad =\frac { 61600\times 7 }{ 22 } =19600\\\ \\ r\quad =\sqrt { 19600 } =\quad 140\quad m\**option (C) is correct**

### (06) Water flows into a tank which is 200 m long and 150 m wide through a pipe of cross-section 0.3 m * 0.2 m at 20km/hr. Then the time (in hrs) for the water level in the tank to reach 8 m is?

a. 50

b. 120

c. 150

d. 200

Read Solution

Volume of water come from pipe in 1 hour = 0.3 m * 0.2 m * 20 * 1000 m

==> 1200 cu meter

After t hours, water is at height of 8 meters

==> volume of water * t hours = length of tank * breadth of tank * height

==> 1200 * t = 200 * 150 * 8

==> t = 200

Hence 200 hours is the required answer

Option (D) is the right answer

### (07) If the area of rectangle is ({ x }^{ 2 }+7x\quad +10) sq. cm, then find the perimeter of rectangle

(a.) 4x+14 cm

(b.) 2x + 14 cm

(c) x+14 cm

(d) 2x+7 cm

Read Solution

**Hence option (A) is the right answer**

### (08) A kite in the shape of a square with diagonal 32 cm attached to an equilateral triangle of base 8 cm. Approximately how much paper has been used to make the kite

a. 539.712 sq cm

b. 538.712

c. 540.712

d. 541.712

Read Solution

Area of square = 1/2 * diagonal * diagonal

==> 1/2 * 32 * 32

==> 512 sq cm

==> 27.712 sq cm

The required area of the Kite = Area of square + Area of equilateral triangle

==> 512 + 27.712

==> 539.712 sq cm

**Hence option (A) is correct**

### (09) How any tiles, each 4 decimeter square, will be required to cover the floor of a room 8 m long and 6 m broad?

a. 200

b. 260

c. 280

d. 300

Read Solution

Length of floor = 8 meter

Breadth of floor = 6 meter

Area of floor = L * B => 8 * 6 => 48 sq m

we know that

1 meter = 10 dm

So, 48 sq m = 48 * 10 * 10 = 4800 sq dm

Area of square tile = side * side = 16 sq dm

Number of tiles = Area of floor/Area of tiles

==> 4800/16

==> 300 tiles

**Hence option (D) is the right answer**

### (10) Length of a side of a square inscribed in a circle is a\sqrt { 2 } units. Find the circumference of the circle

A)\qquad 2\pi a\quad units\qquad\\ \\ B) \pi a\quad units\qquad \qquad\\ \\ C) 4\pi a\quad units\qquad\\ \\ D)\frac { 2a }{ \pi } \quad unitsRead Solution

Hence option (A) is correct