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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

Find the in-radius (in cm) of an equilateral triangle whose sides are 6 cm each.

A) √3	B) 2√3
C) 3√3	D) 4√3

A) √3

B) 2√3

C) 3√3

D) 4√3

Answer & Explanation Answer: A) √3

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1 1079

In a triangle ABC, right angled at B, BC = 15 cm and AB = 8 cm. A circle is inscribed in triangle ABC. Then the radius of the circle is :

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

A) 3 cm

B) 2 cm

C) 4 cm

D) 1 cm

Answer & Explanation Answer: A) 3 cm

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0 1079

PQ is the chord of a circle whose centre is O. ROS is a line segment originating from a point R on the circle that intersect PQ produced at point S such that QS = OR. If ∠QSR = 30°, then what is the value (in degrees)of POR?

A) 30	B) 45
C) 60	D) 90

A) 30

B) 45

C) 60

D) 90

Answer & Explanation Answer: D) 90

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0 1077

What can be the maximum number of common tangent which can be drawn to two non-intersecting circles?

A) 2	B) 4
C) 3	D) 6

A) 2

B) 4

C) 3

D) 6

Answer & Explanation Answer: B) 4

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0 1077

The base and hypotenuse of a right angled triangle is 12 cm and 5 cm respectively. Find the circum-radius (in cm) of the triangle.

A) 5	B) 6
C) 6.5	D) 7

A) 5

B) 6

C) 6.5

D) 7

Answer & Explanation Answer: C) 6.5

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1 1077

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 1074

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 1074

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?