Sample Material of Online Coaching For SSC CGL (Tier - 2) - Volume and Surface Area of Solid Figures


Sample Material SSC CGL TIER-2 Online Coaching


Numerical Aptitude (Chapter: Volume and Surface Area of Solid Figures)

Solid

Anything that occupies space is called a Solid. In addition to area, a solid figure has volume also. It has three dimensions namely, length, breadth and height. For solid two different types of areas namely, lateral surface area or curved surface area and total surface area are defined.

1. Prism

A solid having two congruent and parallel faces, called bases and whose other faces, the lateral faces are parallelograms, formed by joining corresponding vertices of the bases is called a Prism.

2. Right Prism

A prism in which bases are perpendicular to the lateral edges is called a Right Prism. The base of the prism can be a polygon.

In a right prism
(i) Number of lateral surfaces = Number of sides of the base of the prism
(ii) Total number of surfaces of a prism = Number of lateral surfaces + 2
(iii) Lateral surface area = Perimeter of base × Height
(iv) Total surface area = Lateral surface area + 2 (Area of base)
(v) Volume = Area of base × Height

3. Cuboid

A right prism in which the base is a rectangle is called a Cuboid. If l is the length and b the breadth of the base and h the height, then

Lateral surface area = 2 (l + b)h sq unit
Total surface area = 2(l + b)h + 2lb = 2 (lb + bh + lh) sq unit
Volume = lbh cu unit
The longest diagonal of the cuboid =

4. Cube

A right prism in which the base is a square and height is equal to the side of the base is called a cube. If x is the side of the cube, then lateral surface area = 4x × x = 4x2sq unit
Total surface area = 4x2 + 2(x2) = 6x2 sq unit
Volume = x2 × x = x3 cu unit
The longest diagonal of the cube =

5. Cylinder

If the base of a right prism is circular, then it becomes a cylinder. The lateral surface area c the cylinder is a single curved surface called the curved surface area. If r is the radius of the base and h is the height of the cylinder, then
Curved surface area = 2Πrh sq unit
Total surface area = 2Πrh + 2Πr2 = 2Πr (r + h) sq unit
Volume of cylinder = Πr2h cu unit

6. Cone

If the base of a right pyramid is circular, then it becomes a cone. The lateral surface area of the cone is a single curved surface. If r is the radius of the base h is the height of the cone and l the slant height of the cone, then slant height, unit
Curved surface area = Πrl sq unit
Total surface area = Πrl + Πr2 = Πr (l + r) sq unit

Volume of cylinder = 1Πr2h cu unit.
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:: Home Assignment for Practice ::

1. A rectangular water tank is 80 m × 40 m. Water flows into it through a pipe 40 sq. cm at the opening at a speed of 10 km/hr. By how much, the water level will rise in the tank in half an hour?

(a)4/11cm
(b)5/9 cm
(c)5/8 cm
(d)4/5 cm

2. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of areas of the four walls, the volume of the hall is:

(a) 720
(b) 800
(c) 1200
(d) 2000

3. The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is cm. Its surface area is:

(a) 127 cm2
(b) 236 cm2
(c) 361 cm2
(d) 480 cm2

4. A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is:

(a) 309 m3
(b) 270 m3
(c) 360 m3
(d) 607 m3

5. A metallic sheet is of rectangular shape with dimensions 48 m × 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:

(a) 5835
(b) 5120
(c) 6420
(d) 9260

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