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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

Curved surface area of a cylinder is 528 sq cm. If circumference of its base is 44 cm, find the height of the cylinder?

A) 12 cm	B) 24 cm
C) 36 cm	D) 6 cm

A) 12 cm

B) 24 cm

C) 36 cm

D) 6 cm

Answer & Explanation Answer: A) 12 cm

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1 1677

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)

A) 16 cm	B) 4 cm
C) 8 cm	D) 12 cm

A) 16 cm

B) 4 cm

C) 8 cm

D) 12 cm

Answer & Explanation Answer: C) 8 cm

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1 1672

The length of diagonal of a square is 9√2 cm. The square is reshaped to form a triangle. What is the area (in sq.cm) of largest in circle that can be formed in that triangle?

A) 6π	B) 9π
C) 12π	D) 15π

A) 6π

B) 9π

C) 12π

D) 15π

Answer & Explanation Answer: C) 12π

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0 1671

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 1670

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 1646

The measure of the four successive angles of a quadrilateral are in the ratio 7 : 11 : 7 : 11. The quadrilateral is a ______.

A) trapezium	B) rectangle
C) parallelogram	D) square

A) trapezium

B) rectangle

C) parallelogram

D) square

Answer & Explanation Answer: C) parallelogram

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0 1642

The ratio of the volume of two cylinders is 7 : 3 and the ratio of their heights is 7 : 9. If the area of the base of the second cylinder is 154 sq. cm, then what will be the radius (in cm) of the first cylinder?