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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

If the volume of a cylinder is 3850 cubic cm and height is 25 cm, what is its radius? (Take π = 22/7)

A) 7 cms	B) 14 cms
C) 10 cms	D) 3.5 cms

A) 7 cms

B) 14 cms

C) 10 cms

D) 3.5 cms

Answer & Explanation Answer: A) 7 cms

Explanation:

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2 1657

In ΔPQR, PQ = PR = 18 cm, AB and AC are parallel to lines PR and PQ respectively. If A is the mid-point of QR, then what is the perimeter (in cm) of quadrilateral ABPC?

A) 18	B) 28
C) 32	D) 36

A) 18

B) 28

C) 32

D) 36

Answer & Explanation Answer: D) 36

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3 1657

In triangle PQR, the sides PQ and PR are produced to A and B respectively. The bisectors of ∠AQR and ∠BRQ intersect at point O. If ∠QOR = 50°, then what is the value (in degrees) of ∠QPR?

A) 50	B) 60
C) 80	D) 100

A) 50

B) 60

C) 80

D) 100

Answer & Explanation Answer: C) 80

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0 1652

The diameters of two cylinders are in the ratio 3:2 and their volumes are equal. The ratio of their heights is

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

A) 2:3

B) 3:2

C) 9:4

D) 4:9

Answer & Explanation Answer: D) 4:9

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2 1649

In the given figure, the length of arc BC of the given circle is 44 cm. If O is the centre of circle, then what is the radius (in cm) of the circle?

A) 7	B) 14
C) 28	D) 35

A) 7

B) 14

C) 28

D) 35

Answer & Explanation Answer: C) 28

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0 1645

ΔXYZ is similar to ΔPQR. If ratio of Perimeter of ΔXYZ and Perimeter of ΔPQR is 4:9 and if PQ = 27 cm, then what is the length of XY (in cm)?

A) 9	B) 12
C) 16	D) 15

A) 9

B) 12

C) 16

D) 15

Answer & Explanation Answer: B) 12

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1 1644

What will be the sum of the measures all the interior angles of a polygon having 14 sides?

A) 2520°	B) 2160°
C) 2880°	D) 3240°

A) 2520°

B) 2160°

C) 2880°

D) 3240°

Answer & Explanation Answer: B) 2160°

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0 1641

A solid brass sphere of radius 2.1 dm is converted into a right circular cylindrical rod of length 7cm. The ratio of total surface areas of the rod to the sphere is