surface area and its volume class9 most important questions

 Find the curved surface area of a circular area of ​​a right circular cone whose slant height is 10 cm and the radius of the base is 7 cm

curved surface area of cone = πrl

                   22/7 * 7 * 10

                   Answer =220

Find the total surface area of ​​a hemisphere of radius 10 cm

                         total surface area of ​​a hemisphere=3πr2

                       3*3.14*10*10

                          Answer  =  942

Write 4=5x-3y in the form ax +by +c=0 and find the values ​​of a b and c

ax +by+c =0

5x +(-3y)=4

5x-3y-4=0

a=5

b=-3

c=-4

When a spherical balloon is filled with air, its radius increases from 7cm to 14cm, find the ratio of the area of ​​the balloon in these two cases

curved surface area of sphere = 4πr²

Radius 7cm                                           Radius 14cm 

       = 4π(r₁)²                                           = 4π(r₁)²

                    = 4π(r₁)²/4π(r₂)²

                     = (r₁)²/(r₂)²

                        = (r₁/r₂)²

                        = (7/14)²

                         = (1/2)²

                           = (1/4)

                            = 1:4

The ratio of the sides of a triangular plot is 3:5:7. and its perimeter is 300 m. Find the area of ​​the plot.

                                                    Perimeter = 3x+5x+7x

                                                  300 = 15x

                                                  x = 300/15

                                                       x = 20.

                                                      a=3x=3×20

= 60m.

b=5x=5×20

= 100m.

c=7x=7×20

= 140m.

 s = a+b+c/2

= 60+100+140/2

= 300/2

= 150m.

Area = √s(s-a)(s-b)(s-c)

= √150(150-60)(150-100)(150-140)

= √150×90×50×10

= √30×5×30×3×5×10×10

= 30×5×10√3

= 1500√3