CURVED SURFACE AREA AND TOTAL SURFACE AREA OF CONE

Curved surface area :  =  πrl Total surface area of  =  πr(l + r)

Example 1 :

A right angled triangle PQR where angle Q = 90 degree is rotated about QR and PQ. If QR = 16 cm and PR = 20 cm, compare the curved surface areas of the right circular cones so formed by the triangle.

Solution :

radius of cone  =  16 cm 

Slant height  =  20 cm

If the triangle is rotated about PQ :

Curved surface area =  Πrl

  =  Π ⋅ 16 ⋅ 20

  =  320Π cm²

height  =  √(l² - r²)

 =  √(20² - 16²)

 =  √144

h  =  12

If the triangle is revolved about QR, then radius will be 12 cm

Curved surface area =  Πrl

  =  Π ⋅ 12 ⋅ 20

  =  240Π cm²

So, curved surface area of cone is larger when it is revolved about PQ.

Example 2 :

4 persons live in a conical tent whose slant height is 19 cm. If each person require 22 cm² of the floor area, then find the height of the tent.

Solution :

Slant height of conical tent  =  19 cm

Required area of floor for 1 person  =  22 cm²

Area for 4 persons  =  22(4)  =  88

Πr²  =  88

(22/7) ⋅ r²  =  88

r²  =  88 ⋅ (7/22)

r  =  2√7

height  =  √(l² - r²)

 =  √(19² - (2√7)²

 =  √[361 - 4(7)]

h  =  √333

h = 18.25 cm

Example 3 :

A girl wishes to prepare birthday caps in the form of right circular cones for her birthday party, using a sheet of paper whose area is 5720 cm², how many caps can be made with radius 5 cm and height 12 cm.

Solution :

r = 5 cm, height of cap  =  12 cm

slant height =  √(r² + h²)

 =  √(5² + 12²)

 =  √(25 + 144)

h  =  √169

h = 13

Area of sheet  =  5720 cm²

Curved surface area of one cap  =  Πrl

  =  (22/7) ⋅ 5 ⋅ 13  -----(1)

Required number of cups  =  5720 / [ (22/7) ⋅ 5 ⋅ 13]

=  (5720 ⋅ 7)/(22 ⋅ 5 ⋅ 13)

=  28 cups

Example 4 :

The ratio of the radii of two right circular cones of same height is 1:3. Find the ratio of their curved surface area when the height of each cone is 3 times the radius of the smaller cone.

Solution :

r₁  =  1, r₂  =  3

Height of 1^st cone  =  3(radius of smaller cone)

  =  3(1)  =  3

Height of 2^nd cone  =  3(radius of smaller cone)

  =  3(1)  =  3

Slant height of 1st cone  =   √(r² + h²)

=   √(1² + 3²)

=   √10

Slant height of 1st cone  =   √(r² + h²)

=   √(3² + 3²)

=   √18  =  3√2

Curved surface area  =  Πrl

Πr₁l₁ : Πr₁l₁

1√10 : 3 (3√2)

√10 : 9√2

√5 : 9

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.