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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

A cylindrical vessel of radius 7 cm is partially filled with water. By how much will the water level rise if a sphere of radius 6 cm is completely immersed in this water?

A) 11.76 cm	B) 17.64 cm
C) 23.52 cm	D) 5.88 cm

A) 11.76 cm

B) 17.64 cm

C) 23.52 cm

D) 5.88 cm

Answer & Explanation Answer: D) 5.88 cm

Explanation:

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0 1165

In triangle ABC measure of angle B is 90 deg. If sinA = 24/25, and AB = 1.4cm, then what is the length (in cm) of side BC.

A) 4.8	B) 5
C) 3	D) 5.6

A) 4.8

B) 5

C) 3

D) 5.6

Answer & Explanation Answer: A) 4.8

Explanation:

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3 1164

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

Explanation:

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0 1164

The volume of a cuboid is 320 cubic cm. Find its total surface area if its length and breadth are 10 cm and 8 cm respectively?

A) 608 sq cms	B) 304 sq cms
C) 152 sq cms	D) 456 sq cms

A) 608 sq cms

B) 304 sq cms

C) 152 sq cms

D) 456 sq cms

Answer & Explanation Answer: B) 304 sq cms

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1 1163

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.