Question

how to do by method.

Answer 1

r : h = 4 : 3
Area of base = 154 cm²
πr² = 154
r² = 154 * 7 / 22
r = √7 * 7
r = 7 cm

h = 3 / 7 * r
h = 3/7 * 7

h = 3 cm

Answer 2

Let the common ratio be x.

Given that radius of the cone = 4x.  ------- (1)

Given that height of the cone = 3x.  ----- (2)

The slant height of the cone = root 4x^2 + 3x^2

                                                = root 16x^2 + 9x^2

                                                = root 25x^2

                                              l  = 5x.   ----------- (3)

Given that Area of the base = 154cm^2.

We know that Area of the base = pir^2.

pir^2 = 154

22/7 * (4x)^2 = 154

22/7 * 16x^2 = 154

352x^2/7 = 154

352x^2 = 154 * 7

352x^2 = 1078

x^2 = 1078/352

x^2 = 49/16

x = 7/4

x = 1.75 (or) x = -1.75.

As x cannot be -ve, so x = 1.75.


On substituting x in (1),(2) & (3), we get

 Radius = 4 * 1.75

              = 7


Height = 3 * 1.75

            = 5.25.


Slant height = 5 * 1.75

                      = 8.75


Now,

 We know that Area of the curved surface = pirl

                                                                       = 22/7 * 7 * 8.75

                                                                       = 192.5cm^2.


Therefore the area of the curved surface area = 192.5cm^2.


Hope this helps!