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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:

What is the area (in sq cm) of a regular hexagon of side 14 cm?

A) 147√3 B) 441√3
C) 196√3 D) 294√3
 
Answer & Explanation Answer: D) 294√3

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Q:

ABCD is a cyclic quadrilateral of which AB is the diameter. Diagonals AC and BD intersect at E. If ∠DBC = 35°, Then ∠AED measures

A) 35° B) 45°
C) 55° D) 90°
 
Answer & Explanation Answer: C) 55°

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Q:

What is the slope of the line perpendicular to the line passing through the points (­-4,5) and (3,­-2)?

A) 2 B) 3/7
C) -3/7 D) 1
 
Answer & Explanation Answer: D) 1

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Q:

The sum of the lengths of the edges of a cube is equal to four times the perimeter of a square. If a quarter of the numerical value of the volume of the cube is equal to the numerical value of the area of the square, then the length of one side of the square is

A) 27/16 units B) 10.5 units
C) 9/4 units D) 27 units
 
Answer & Explanation Answer: A) 27/16 units

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Q:

Two circles with centres P and Q touch each other externally. A straight line drawn through the point of contact intersects the circle with centre P at A and the circle with centre Q at B. Then, which of the following is true?

A) AP = BQ B) AP | BQ
C) AP || BQ D) AP = 1⁄2 BQ
 
Answer & Explanation Answer: C) AP || BQ

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Q:

In a rectangle

A) Diagonals bisect opposite angles B) Consecutive sides are congruent
C) All sides are congruent D) Diagonals form two congruent triangles
 
Answer & Explanation Answer: D) Diagonals form two congruent triangles

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Q:

If the measure of the interior angle of a regular polygon is 100 deg greater than the measure of its exterior angle then how many sides does it have?

 

A) 10 B) 12
C) 9 D) 15
 
Answer & Explanation Answer: C) 9

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Q:

The copper wire when bent in the form of a square encloses an area of 121 cub.cm. If the same wire is bent into the form of a circle, find the area of the circle.

A) 154 sq.cm B) 153 sq.cm
C) 155 sq.cm D) 150 sq.cm
 
Answer & Explanation Answer: A) 154 sq.cm

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