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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

In the two triangles ABC and DEF the sides AB = DE and BC = EF. Which of the following option is correct which results in the $∆ ABC ≅ ∆ DEF$ ?

A) 1	B) 2
C) 3	D) 4

A) 1

B) 2

C) 3

D) 4

Answer & Explanation Answer: D) 4

Explanation:

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0 1064

ΔABC is similar to ΔDEF. Length of AB is 18 cm and length of the corresponding side DE is 10 cm. What is the ratio of Perimeter of ΔABC : Perimeter of ΔDEF?

A) 5:9	B) 9:5
C) 81:25	D) 25:81

A) 5:9

B) 9:5

C) 81:25

D) 25:81

Answer & Explanation Answer: B) 9:5

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0 1060

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 1060

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:3, what is the ratio of area of ΔADE and area of quadrilateral BDEC?

A) 4 : 21	B) 4 : 25
C) 4 : 29	D) 4 : 9

A) 4 : 21

B) 4 : 25

C) 4 : 29

D) 4 : 9

Answer & Explanation Answer: A) 4 : 21

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0 1053

ΔABC is right angled at B. BD is the altitude. AD is 8 cm and DC is 50 cm. What is the length of BD?

A) 25 cm	B) 20 cm
C) 16 cm	D) 15 cm

A) 25 cm

B) 20 cm

C) 16 cm

D) 15 cm

Answer & Explanation Answer: B) 20 cm

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0 1051

The lengths of the two diagonals of a rhombus are 7 cm and 24 cm. Find the length of its perimeter (in cm).

A) 25	B) 100
C) 75	D) 50

A) 25

B) 100

C) 75

D) 50

Answer & Explanation Answer: D) 50

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1 1047

Slope of the side DA of the rectangle ABCD is 1/3. What is the slope of the side AB?

A) 3	B) 1/3
C) -1/3	D) -3

A) 3

B) 1/3

C) -1/3

D) -3

Answer & Explanation Answer: D) -3

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0 1039

Two circles touch each other externally. The distance between their centres is 7 cm. If the radius of one circle is 4 cm, then the radius of the other circle will be