Volume and Surface Area MCQ

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

(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

(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

(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

(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

(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

Area\quad of\quad equilateral\quad triangle\quad =\frac { \sqrt { 3 } }{ 4 } side^{ 2 }\\\ \\\quad =\frac { \sqrt { 3 } }{ 4 } 8^{ 2 }

==> 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

Given,\\ \\ side\quad of\quad square\quad =\quad a\sqrt { 2 } units.\\\ \\ diagonal^{ 2 }\quad =\quad { a\sqrt { 2 } }^{ 2 }\quad +\quad { a\sqrt { 2 } }^{ 2 }\quad =2{ a }^{ 2 }\quad +2{ a }^{ 2 }\quad =4{ a }^{ 2 }\\\ \\ Therefore,\quad diagonal\quad =\quad \sqrt { 4{ a }^{ 2 } } \quad =2a\quad units\quad =\quad diameter\\\ \\ circumference\quad =\quad 2\pi r\quad =\quad 2\pi \times \frac { 2a }{ 2 } =\quad 2a\pi \quad units.

Hence option (A) is correct