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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

The two equal sides of an isosceles triangle is 20 cm each and the third side is 30 cm. What is the area (in sq.cm) of the triangle?

A) 50√5	B) 100
C) 75√7	D) 175

A) 50√5

B) 100

C) 75√7

D) 175

Answer & Explanation Answer: C) 75√7

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0 484

Slope of the line AB is 4/3. Co-ordinates of points A and B are (x , -5) and (2 , -3) respectively. What is the value of x?

A) 1/2	B) -1/4
C) 4	D) -4

A) 1/2

B) -1/4

C) 4

D) -4

Answer & Explanation Answer: A) 1/2

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0 483

What is the slope of the line parallel to the line passing through the points (6,3) and (2,1)?

A) -1/2	B) -1
C) 2	D) 1

A) -1/2

B) -1

C) 2

D) 1

Answer & Explanation Answer: A) -1/2

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0 482

In a triangle, the length of the side opposite the angle which measures 45° is 16 cm, what is the length of the side opposite to the angle which measures 90°?

A) 8√3 cm	B) 16√2 cm
C) 8 cm	D) 16√3 cm

A) 8√3 cm

B) 16√2 cm

C) 8 cm

D) 16√3 cm

Answer & Explanation Answer: B) 16√2 cm

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0 481

A wheel has diameter 84 cm. The number of complete revolution it will take to cover 792 m is

A) 330	B) 300
C) 320	D) 350

A) 330

B) 300

C) 320

D) 350

Answer & Explanation Answer: B) 300

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0 480

In the circle above, chord AB is extended to meet the tangent DE at D. If AB = 5 cm and DE = 6 cm, find the length of BD.

A) 4 cm	B) 5 cm
C) 6 cm	D) √30 cm

A) 4 cm

B) 5 cm

C) 6 cm

D) √30 cm

Answer & Explanation Answer: A) 4 cm

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0 479

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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0 477

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°?