Worked out Examples
The ratio of the length and the breadth of a rectangle is 3 : 2.
If the perimeter of the rectangle is equal to the perimeter of a square, what
is the ratio of their areas? .
Let the length and breadth of the rectangle
be 3x and 2x. Given that, .
2(3x + 2x) = 4s ⇒ s = 5x/2
Ratio of their areas = (3x x 2x) :
= 24 : 25. .
The difference in the areas of two concentric circles is 22 sq.
units and radius of outer circle is 4 units. What is the radius of inner
Given that the circles are concentric. Radius of outer circle is 4
units, let the radius of inner circle be r. Difference in their areas = 22 sq.
pR2 - pr2 =
p(4)2 - pr2 =
22 = pr2
x 9 = pr2
p x 32 = pr2
r2 = 32 . r = 3 units .
The dimensions of a cuboid are
15 cm x 12 cm x 10 cm. .
What is the total surface area?
The total surface area of a cuboid
= 2 [lb + bh + hl]
= 2 (15)(12) + (12)(10) + (10)(15)] = 900 cm2
The radius of the base of a cone is 14 cm and its vertical height
is 48 cm. What is the curved surface area of the cone? .
Curved surface area of a cone = prl, where r is the radius and 1 is the slant height. .
1 = = = 50 cm.
Curved surface area of the cone = prl
= 22/7 x 14 x 50 = 2200 sq. cm .
A right cone frustum with height being 5 cm, has radii of its top
and bottom surfaces as 7 cm and 12 cm respectively. What is the volume of the
Let r1 = 7 cm, r2 = 12 cm, h = 5 cm he the
given dimensions of the cone frustum. The volume of the frustum is given by .
V = (p(12)2 . (5 + h) – p(7)2. h)
= p [144(5 + h) - 49h] = p [720 + 144h - 49h]
= p [720 + 95h] … -O’OA » -OP’A’
⇒ ⇒ 12h = 7h + 35
⇒ 5h = 35 ⇒ h = = 7cm
\ Volume of the body = p [720 + 95(7)]
= p  = pcu . cm