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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

ΔABC is similar to ΔDEF. Length of AB is 12 cm and length of the corresponding side DE is 8 cm. What is the ratio of Perimeter of ΔABC : Perimeter of ΔDEF?

A) 9:4	B) 4:9
C) 3:2	D) 2:3

A) 9:4

B) 4:9

C) 3:2

D) 2:3

Answer & Explanation Answer: C) 3:2

Explanation:

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0 685

If the in radius of the equilateral triangle is 8 cm then what is the value of circum radius (in cm) of the triangle?

A) 8	B) 16
C) 18	D) 20

A) 8

B) 16

C) 18

D) 20

Answer & Explanation Answer: B) 16

Explanation:

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Exam Prep: Bank Exams , CAT

0 682

O is an centre of a circle. P is an external point of it at distance of 13cm from O. The radius of the circle is 5cm. Then the length of a tangent to the circle from P upto the point of contact is

A) √194cm	B) 10cm
C) 12cm	D) 8cm

A) √194cm

B) 10cm

C) 12cm

D) 8cm

Answer & Explanation Answer: C) 12cm

Explanation:

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0 680

The length of the diameter of the circle is 10 cm and length of the chord drawn in a circle is 6 cm. Find the distance (in cm) of chord from the center.

A) 10	B) 8
C) 6	D) 4

A) 10

B) 8

C) 6

D) 4

Answer & Explanation Answer: D) 4

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0 678

Find the volume (in cm3) of a cuboid of length, breadth and height of 10.5 cm, 8 cm and 9 cm respectively.

A) 307	B) 541
C) 355	D) 756

A) 307

B) 541

C) 355

D) 756

Answer & Explanation Answer: D) 756

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0 678

The co-ordinates of the centroid of a triangle ABC are (1 , -4). What are the co-ordinates of vertex C if co-ordinates of A and B are (3 , -4) and (0 , 5) respectively?