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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

In the given figure, AB, AE, EF, FG and GB are semicircles. AB = 56 cm and AE = EF = FG = GB. What is the area (in sq.cm) of the shaded region?

A) 414.46	B) 382.82
C) 406.48	D) 394.24

A) 414.46

B) 382.82

C) 406.48

D) 394.24

Answer & Explanation Answer: D) 394.24

Explanation:

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0 1603

ABC is a right angled triangle in which ∠A = 90°, AB = 5 cm and AC = 12 cm. What is the approximate volume (in cm3) of the double cone formed by rotating the triangle about its hypotenuse?

A) 145	B) 290
C) 435	D) 580

A) 145

B) 290

C) 435

D) 580

Answer & Explanation Answer: B) 290

Explanation:

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1 1602

If curved surface area of a cylinder is 1386 sq cm and height is 21 cm, what will be its radius? (Take π = 22/7)

A) 21 cms	B) 5.25 cms
C) 10.5 cms	D) 15.75 cms

A) 21 cms

B) 5.25 cms

C) 10.5 cms

D) 15.75 cms

Answer & Explanation Answer: C) 10.5 cms

Explanation:

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1 1599

D, E, F are the mid - points of the sides BC , CA and AB respectively of a ΔABC . Then the ratio of the areas of ΔDEF and ΔABC is

A) 1/2	B) 1/4
C) 1/8	D) 1/16

A) 1/2

B) 1/4

C) 1/8

D) 1/16

Answer & Explanation Answer: B) 1/4

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0 1592

If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two chords?

A) 1 cm or 7 cm	B) 2 cm or 14 cm
C) 3 cm or 21 cm	D) 4 cm or 28 cm

A) 1 cm or 7 cm

B) 2 cm or 14 cm

C) 3 cm or 21 cm

D) 4 cm or 28 cm

Answer & Explanation Answer: B) 2 cm or 14 cm

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1 1589

A cylindrical vessel of radius 6 cm is partially filled with water. By how much will the water level rise if a sphere of radius 5 cm is completely immersed in this water? (Take π = 22/7)

A) 6.67 cm	B) 5.56 cm
C) 6.94 cm	D) 4.63 cm

A) 6.67 cm

B) 5.56 cm

C) 6.94 cm

D) 4.63 cm

Answer & Explanation Answer: D) 4.63 cm

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Exam Prep: AIEEE , Bank Exams , CAT

1 1579

Three solid spheres have their radii r1, r2 and r3. The spheres are melted to form a solid sphere of bigger radius. Then the radius of the new sphere is