99+ Solved Volume and Surface Area Questions and Answers (2025)

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Important Formulae

FACTS AND FORMULAE FOR VOLUME AND SURFACE AREA QUESTIONS

I. CUBOID

Let length=l, breadth =b and height =h units. Then,

1.Volume = (l x b x h)

2.Surface area = 2(lb +bh + lh) sq.units

3.Diagonal= $\sqrt{l^{2} + b^{2} + h^{2}}$ units

II. CUBE

Let each edge of a cube be of length a. Then,

1.Volume = $a^{3}$ cubic units.

2.Surface area = $6 a^{2}$ sq.units

3.Diagonal = $\sqrt{3} a$ units

III. CYLINDER

Let radius of base = r and Height (or Length) = h. Then,

1.Volume = $({πr}^{2} h)$ cubic units

2.Curved surface area= $(2 π r h)$ sq.units

3.Total surface area= $(2 πrh + 2 {πr}^{2})$ sq.units

IV. CONE

Let radius of base =r and Height = h. Then,

1.Slant height, $l = \sqrt{h^{2} + r^{2}}$ units

2.Volume = $(\frac{1}{3} {πr}^{2} h)$ cubic units.

3.Curved surface area = $(πrl)$ sq.units

4.Total surface area = $(πrl + {πr}^{2})$ sq.units

V. SPHERE

Let the radius of the sphere be r. Then,

1.Volume= $(\frac{4}{3} {πr}^{3})$ cubic units

2.Surface area = $(4 {πr}^{2})$ sq.units

VI. HEMISPHERE

Let the radius of a hemisphere be r. Then,

1.Volume = $(\frac{2}{3} {πr}^{3})$ cubic units.

2.Curved surface area = $(2 {πr}^{2})$ sq.units

3.Total surface area = $(3 {πr}^{2})$ sq.units

For the circle shown below, find the length (in cm) of the largest cord of the circle.

A) 8	B) 12
C) 16	D) 18

Answer & Explanation Answer: C) 16

Explanation:

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Exam Prep: Bank Exams

1 108486

If each edge of a cube is increased by 50%, find the percentage increase in Its surface area

A) 125%	B) 150%
C) 175%	D) 110%

Answer & Explanation Answer: A) 125%

Explanation:

Let the edge = a cm

So increase by 50 % = a + a/2= 3a/2

Total surface Area of original cube = $6 a^{2}$

TSA of new cube = $6 {(\frac{3 a}{2})}^{2}$ = $6 (\frac{9 a^{2}}{4})$ = $13.5 a^{2}$

Increase inarea = $13.5 a^{2} - 6 a^{2}$ = $7.5 a^{2}$

$7.5 a^{2}$ Increase % = $\frac{7.5 a^{2}}{6 a^{2}} \times 100$ = 125%

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480 85927

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

A) 12 pi cub.cm	B) 15 pi cub.cm
C) 16 pi cub.cm	D) 20 pi cub.cm

Answer & Explanation Answer: A) 12 pi cub.cm

Explanation:

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105 52185

Arectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

A) 30	B) 40
C) 10	D) 20

Answer & Explanation Answer: B) 40

Explanation:

Volume of the block = (6 x 12 x 15) cu.cm = 1080cu.cm

Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm

= 3 cm.

Volume of this cube = (3 x 3 x 3) cu.cm = 27cu.cm

Number of cubes = $\frac{1080}{27}$ = 40.

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126 50041

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 cu.m, then the rise in the water level in the tank will be:

A) 20 cm	B) 25 cm
C) 35 cm	D) 50 cm

Answer & Explanation Answer: B) 25 cm

Explanation:

Total volume of water displaced =(4 x 50) cu.m= 200 cu.m

Rise in water level = $(\frac{200}{40 \times 20})$ =0.25m = 25cm

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62 49568

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceilingis equal to the sum of the areas of four walls, the volume of the hall is:

A) 720	B) 900
C) 1200	D) 1800

Answer & Explanation Answer: C) 1200

Explanation:

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86 39680

A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

A) 49	B) 50
C) 53.5	D) 55

Answer & Explanation Answer: A) 49

Explanation:

Area of the wet surface = [2(lb + bh + lh) - lb]

= 2(bh + lh) + lb

= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] $m^{2}$

= 49 $m^{2}$

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85 39478

The diagonal of a rectangle is sqrt(41) cm. and its area is 20 sq. cm. The perimeter of the rectangle must be:

A) 9 cm	B) 18 cm
C) 20 cm	D) 41 cm

Answer & Explanation Answer: B) 18 cm

Explanation:

$l^{2} + b^{2}$ = ${(d i a g o n a l)}^{2}$ =40

Also, lb=20

${(l + b)}^{2} = l^{2} + b^{2} + 2 l b$ = 41 + 40 =81

(l + b) = 9.

Perimeter = 2(l + b) = 18 cm.

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47 34318

99+ Solved Volume and Surface Area Questions and Answers (2025)

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