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 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 =l2+b2+h2 units

 

 

II. CUBE 

Let each edge of a cube be of length a. Then,

1. Volume = a3 cubic units.

2. Surface area = 6a2 sq.units

3. Diagonal = 3a units

 

 

III. CYLINDER 

Let radius of base = r and Height (or Length) = h. Then, 

1.Volume = πr2h cubic units 

2. Curved surface area = 2πrh sq.units

3. Total surface area = 2πrh+2πr2 sq.units

 

 

IV. CONE 

Let radius of base =r and Height = h. Then, 

1. Slant height, l=h2+r2 units

 

2. Volume = 13πr2h cubic units.

 

3. Curved surface area = πrlsq.units 

 

4. Total surface area = πrl+πr2sq.units

 

 

V. SPHERE 

Let the radius of the sphere be r. Then, 

1. Volume =43πr3 cubic units

2. Surface area = 4πr2 sq.units

 

 

VI. HEMISPHERE 

Let the radius of a hemisphere be r. Then, 

1. Volume = 23πr3 cubic units.

2. Curved surface area = 2πr2 sq.units

3. Total surface area = 3πr2 sq.units

 

Q:

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.

What is the ratio of the volume of the sphere to that of cone?

A) 6√3:1 B) 7 : 2
C) 3√3:1   D) 5√3:1
 
Answer & Explanation Answer: A) 6√3:1

Explanation:
The top view of the given assembly will look like the figure above
Outermost is the sphere. Inside that there is a cube and within that there is a cone and cylinder with same radius.
Here side of cube = a
Diameter of Sphere = body diagnol = √3 a
Radius of sphere = √3 a/2 =r1
Height of Cylinder = Height of cone = side of cube = a =h
Radius of cylinder = Radius of cone = side of cube/2 = a/2 =r2(as shown in the figure)
Volume of sphere/volume of cone = 43πr1313πr22h = 6√3:1
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Q:

In ΔPQR, PS and PT are bisectors of ∠QPR and ∠QPS respectively. If ∠QPT = 30°, PT = 9 cm and TR = 15 cm, then what is the area (in cm2) of ΔPTR

A) 36 B) 54
C) 72 D) 216
 
Answer & Explanation Answer: B) 54

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0 1541
Q:

In Δ ABC , if ∠BAC = 90° and AB = AC , then ∠ABC is

A) 30° B) 60°
C) 45° D) 25°
 
Answer & Explanation Answer: C) 45°

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0 1541
Q:

An inverted conical shaped vessel is filled with water to its brim. The height of the vessel is 8 cm and radius of the open end is 5 cm . When a few solid spherical metallic balls each of radius 1⁄2 cm are dropped in the vessel , 25% water is overflowed. The number of balls is:

A) 100 B) 400
C) 200 D) 150
 
Answer & Explanation Answer: A) 100

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0 1539
Q:

Find the volume (in cm3) of a cube of side 7.5 cm.

A) 421.875 B) 77.145
C) 39.245 D) 24.435
 
Answer & Explanation Answer: A) 421.875

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0 1537
Q:

What is the reflection of the point (-4, 3) in the line x = -2?

A) (-4 , -7) B) (4 , 3)
C) (0 , 3) D) (-4 , 7)
 
Answer & Explanation Answer: C) (0 , 3)

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1 1536
Q:

If the diameter of a hemisphere is 21 cm, then what is the volume (in cub.cm) of hemisphere?

A) 2810 B) 1250.5
C) 1725.25 D) 2425.5
 
Answer & Explanation Answer: D) 2425.5

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0 1532
Q:

Find the curved surface area (in cm2) of a right circular cylinder of diameter 28 cm and height 12 cm.

A) 968 B) 924
C) 856 D) 1056
 
Answer & Explanation Answer: D) 1056

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0 1530