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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

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

Explanation:

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0 758

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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0 758

What is the sum of the measures of all the interior angles of a regular polygon of 5 sides?

A) 720	B) 1080
C) 1260	D) 540

A) 720

B) 1080

C) 1260

D) 540

Answer & Explanation Answer: D) 540

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0 754

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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0 754

The diameter of the driving wheel of a cart is 154 cm. Calculate the revolution per minute [RPM] of the wheel in order to keep a speed of 33 kmph?

A) 114	B) 112
C) 110	D) 108

A) 114

B) 112

C) 110

D) 108

Answer & Explanation Answer: A) 114

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0 754

Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of AP:PB is 1:4 and area of Δ APQ is 4 sq cm, what is the area of trapezium PQCB?

A) 60 sq cm	B) 16 sq cm
C) 96 sq cm	D) 21 sq cm

A) 60 sq cm

B) 16 sq cm

C) 96 sq cm

D) 21 sq cm

Answer & Explanation Answer: C) 96 sq cm

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0 752

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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0 752

The co-ordinates of the centroid of a triangle ABC are (1 , -4). What are the co-ordinates of vertex C if co-ordinates of A and B are (3 , -4) and (0 , 5) respectively?