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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

Volume of a cylinder is 2310 cubic cm. If circumference of its base is 44 cm, find the curved surface area of the cylinder?

A) 660 sq cm	B) 1320 sq cm
C) 1980 sq cm	D) 330 sq cm

A) 660 sq cm

B) 1320 sq cm

C) 1980 sq cm

D) 330 sq cm

Answer & Explanation Answer: A) 660 sq cm

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1 882

In triangle ABC, ∠ABC = 90°. BP is drawn perpendicular to AC. If ∠BAP = 30°, then what is the value (in degrees) of ∠PBC?

A) 30	B) 36
C) 45	D) 60

A) 30

B) 36

C) 45

D) 60

Answer & Explanation Answer: A) 30

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0 881

The diagonal of a square is 10 cm. What is the length (in cm) of its side?

A) 5	B) 5√2
C) 10√2	D) 5/√2

A) 5

B) 5√2

C) 10√2

D) 5/√2

Answer & Explanation Answer: B) 5√2

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0 880

A prism has a regular hexagonal base with side 6 cm. If the total surface area of prism is 216√3 cm2, then what is the height (in cm) of prism?

A) 3√3	B) 6√3
C) 6	D) 3

A) 3√3

B) 6√3

C) 6

D) 3

Answer & Explanation Answer: A) 3√3

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0 878

Δ ABC is right angled at B. If m∠A = $30 °$ , what is the length of AB (in cm), if AC = 10 cm?

A) 5	B) 5√3
C) 10√3	D) 10

A) 5

B) 5√3

C) 10√3

D) 10

Answer & Explanation Answer: B) 5√3

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0 877

The chord AB of a circle of centre O subtends an angle θ with the tangent at A to the circle. Then measure of∠ABO is

A) θ	B) 90° - θ
C) 90° + θ	D) 2 (180° - θ)

A) θ

B) 90° - θ

C) 90° + θ

D) 2 (180° - θ)

Answer & Explanation Answer: B) 90° - θ

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0 877

Two circles touch each other internally. The radius of the smaller circle is 6 cm and the distance between the centre of two circles is 3 cm. The radius of the larger circle is

A) 7.5 cm	B) 9 cm
C) 8 cm	D) 10 cm

A) 7.5 cm

B) 9 cm

C) 8 cm

D) 10 cm

Answer & Explanation Answer: B) 9 cm

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0 877

If the volumes of two right circular cones are in the ratio 1:4 and their diameters of bases in the ratio 4:5, then their heights will be in the ratio: