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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

Calculate the length (in cm) of PQ, if the radius of the circle is 7 cm and the line through the centre O meets the tangent at point Q such that OP = 25 cm.

A) 20	B) 22
C) 24	D) 26

A) 20

B) 22

C) 24

D) 26

Answer & Explanation Answer: C) 24

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0 920

The point of the intersection of three medians is known as the ____________.

A) circum-centre	B) in-center
C) centroid	D) orthocenter

A) circum-centre

B) in-center

C) centroid

D) orthocenter

Answer & Explanation Answer: C) centroid

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0 917

Calculate the length of the tangent (in cm) which is drawn from a point at a distance of 13 cm from the centre and the largest chord of that circle is 10 cm.

A) 10	B) 12
C) 15	D) 16

A) 10

B) 12

C) 15

D) 16

Answer & Explanation Answer: B) 12

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0 915

If the edge of a cube is increased by 2 cm, the volume will increase by 488 cub.cm. What then will be the length of each edge of the cube?

A) 6 cm	B) 8 cm
C) 9 cm	D) 7 cm

A) 6 cm

B) 8 cm

C) 9 cm

D) 7 cm

Answer & Explanation Answer: B) 8 cm

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0 915

Find the curved surface area (in cm2) of a right circular cylinder of diameter 7 cm and height 6 cm.

A) 132	B) 110
C) 92	D) 154

A) 132

B) 110

C) 92

D) 154

Answer & Explanation Answer: A) 132

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0 910

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 1:2 and area of ΔABC is 45 sq cm, what is the area (in sq cm) of quadrilateral BDEC?

A) 20	B) 40
C) 15	D) 30

A) 20

B) 40

C) 15

D) 30

Answer & Explanation Answer: B) 40

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0 908

An angle is greater than its complementary angle by 40°. Find the measure of the angle?

A) 25°	B) 65°
C) 130°	D) 50°

A) 25°

B) 65°

C) 130°

D) 50°

Answer & Explanation Answer: B) 65°

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0 908

A triangle is circumscribed on the circle of centre O in such a way that sides AB = 12 cm, BQ = 7 cm and CQ = 5 cm. Calculate the lengtth (in cm) of side AC.