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Volume and Surface Area

Volume and Surface Area Questions

Popular Latest Rated 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

If the volume of a cylinder is 3850 cubic cm and height is 25 cm, what is its radius? (Take π = 22/7)

A) 7 cms	B) 14 cms
C) 10 cms	D) 3.5 cms

A) 7 cms

B) 14 cms

C) 10 cms

D) 3.5 cms

Answer & Explanation Answer: A) 7 cms

Explanation:

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2 1150

ΔABC is an equilateral triangle and D, E are midpoints of AB and BC respectively. Then the area of ΔABC : the area of the trapezium ADEC is

A) 5:3	B) 4:1
C) 8:5	D) 4:3

A) 5:3

B) 4:1

C) 8:5

D) 4:3

Answer & Explanation Answer: D) 4:3

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1 1149

Two circles are having radii 9 cm and 12 cm. The distance between their centres is 15 cm. What is the length (in cm) of their common chord?

A) 6.8	B) 13.6
C) 7.2	D) 14.4

A) 6.8

B) 13.6

C) 7.2

D) 14.4

Answer & Explanation Answer: D) 14.4

Explanation:

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0 1149

BE and CF are two altitudes of a triangle ABC. If AB = 6 cm , AC = 5 cm and CF = 4 cm , then the length of BE is

A) 4.8 cm	B) 7.5 cm
C) 3.33 cm	D) 5.5 cm

A) 4.8 cm

B) 7.5 cm

C) 3.33 cm

D) 5.5 cm

Answer & Explanation Answer: A) 4.8 cm

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1 1147

The length, breadth and height of a cuboid are in the ratio 19 : 11 : 13. If length is 30 cm more than height, then what is the volume (in cub.cm) of this cuboid?

A) 81510	B) 89665
C) 195300	D) 339625

A) 81510

B) 89665

C) 195300

D) 339625

Answer & Explanation Answer: D) 339625

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0 1147

The total surface area of a hemisphere is 4158 cm2. Find its diameter (in cm).

A) 21	B) 84
C) 42	D) 63

A) 21

B) 84

C) 42

D) 63

Answer & Explanation Answer: B) 84

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1 1137

From the circumcentre I of the triangle ABC, perpendicular ID is drawn on BC. If ∠BAC = 60°, then the value of ∠BID is

A) 60°	B) 80°
C) 75°	D) 45°

A) 60°

B) 80°

C) 75°

D) 45°

Answer & Explanation Answer: A) 60°

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0 1135

Curved surface area of a cylinder is 1232 sq cm. If circumference of its base is 154 cm, then what will be the height of the cylinder? (Take π = 22/7)