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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 height 7 cm and radius 5 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 8 cm what will be the height of this cone?

A) 8.2 cm	B) 16.4 cm
C) 24.6 cm	D) 32.8 cm

A) 8.2 cm

B) 16.4 cm

C) 24.6 cm

D) 32.8 cm

Answer & Explanation Answer: A) 8.2 cm

Explanation:

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0 638

The line passing through (4,3) and (y,0) is parallel to the line passing through (-1,-2) and (3,0). Find y?

A) -1	B) -2
C) 2	D) -5

A) -1

B) -2

C) 2

D) -5

Answer & Explanation Answer: B) -2

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0 634

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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0 634

If the lengths of the two parallel sides of a trapezium are 7 cm and 9 cm and its area is 80 cm2. Find the distance between its parallel sides (in cm).

A) 5	B) 10
C) 20	D) 15

A) 5

B) 10

C) 20

D) 15

Answer & Explanation Answer: B) 10

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0 633

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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0 629

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

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0 629

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

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0 628

In a triangle, the length of the side opposite the angle which measures 45° is 16 cm, what is the length of the side opposite to the angle which measures 90°?