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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

In a triangle ABC, right angled at B, BC = 15 cm and AB = 8 cm. A circle is inscribed in triangle ABC. Then the radius of the circle is :

A) 3 cm	B) 2 cm
C) 4 cm	D) 1 cm

A) 3 cm

B) 2 cm

C) 4 cm

D) 1 cm

Answer & Explanation Answer: A) 3 cm

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0 886

Calculate the value of $∡$ OBC + $∡$ BAC, if O is the circum-center of the triangle ABC inscribed in the circle.

A) 60 deg	B) 90 deg
C) 120 deg	D) 130 deg

A) 60 deg

B) 90 deg

C) 120 deg

D) 130 deg

Answer & Explanation Answer: B) 90 deg

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0 885

If the lengths of the two parallel sides of a trapezium are 7 cm and 9 cm and its area is 80 cm2. Find the distance between its parallel sides (in cm).

A) 5	B) 10
C) 20	D) 15

A) 5

B) 10

C) 20

D) 15

Answer & Explanation Answer: B) 10

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0 884

In a triangle the length of the side opposite the angle which measures 60° is 15 cm, what is the length of the side opposite to the angle which measures 90°?

A) 15 cm	B) (15√3)/2 cm
C) 10√3 cm	D) 10 cm

A) 15 cm

B) (15√3)/2 cm

C) 10√3 cm

D) 10 cm

Answer & Explanation Answer: C) 10√3 cm

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0 883

The volume of a right circular cone, with a base radius the same as its altitude, and the volume of a hemisphere are equal. The ratio of the radii of the cone to the hemisphere is

A) 2 : 1	B) √2 : 1
C) 23 : 1	D) 33 : 23

A) 2 : 1

B) √2 : 1

C) 23 : 1

D) 33 : 23

Answer & Explanation Answer: C) 23 : 1

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0 882

Δ DEF is right angled at E. If m∠F = 45°, then what is the value of 2 Sin F x Cot F?

A) √2	B) 2
C) 1/√2	D) 1/2

A) √2

B) 2

C) 1/√2

D) 1/2

Answer & Explanation Answer: A) √2

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0 881

Find the volume (in cm3) of a hemisphere of diameter 42 cm.

A) 17832	B) 153512
C) 13858	D) 19404

A) 17832

B) 153512

C) 13858

D) 19404

Answer & Explanation Answer: D) 19404

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0 880

If the lengths of the two parallel sides of a trapezium are 8 cm and 10 cm and its area is 54 cm². Find the distance between its parallel sides (in cm).