Ex 13.3 NCERT Solutions Class 9 Chapter 13




The solutions to exercise 13.3 (from class 9th's maths NCERT book) are given below. The exercise has 8 questions which have been explained thoroughly with proper reasoning.


l= 10 cm

r= 10.5/2 = 5.25 cm


CSA of the cone 

= πrl

= (22/7) x 5.25 x 10

= 22 x 0. 75 x 10

= 22 x 7.5

= 11 x 15

= 165 cm2

TSA of the cone 

= πr (l+ 2r)

= (22/7) x 12 x (21 + 24)

= (22/7) x 12 x 35

= 22 x 12 x 5

= 22 x 60

= 1320 cm2



CSA of cone = 308 cm2

Slant height = 14 cm


(i) CSA = πrl

308 = (22/7) x r x 14

308 = 22 x r x 2

308/22 = 2r

14 = 2r

r = 7 cm


(ii) TSA of cone

= CSA + πr2

= 308 + {(22/7) x 7 x 7}

= 308 + (22 x 7)

= 308 + 154

= 462 


(i)  Slant height of the cone:

l2=h2+r 2  

l2=102+242  

l2=100 + 576

l2=676

l= 26 m




(ii) For the tent no cloth will be used for the base, so we will find the CSA

= πrl

= (22/7) x 24 x 26 m2


Cost of 1 mof canvas = Rs 70


Cost of (22/7)x24 x 26 m2 of canvas

= Rs 70 x (22/7)x24 x 26 

= Rs 10 x 22 x 24 x 26

= Rs 137280





The cloth is in the form of the rectangle, and its area is equal to the CSA of the conical tent.

l2=h2+r 2  

l2=82+6 2  

l2= 64 + 36

l2= 100

l=10  



Let the length of the cloth be n


 CSA = Area of the cloth

Ï€rl = (n) x 3

3.14 x 6 x 10 = 3n

188.4 = 3n

n= 62.8 

n= 63 m


  

The slant height of the cone = 25 m

Radius = 14/2 = 7 m


CSA of the conical tomb 

= πrl

= (22/7) x 7 x 25

= 22 x 25

= 550 m2


Cost of whitewashing 100 m2 CSA of the conical tomb

    = Rs 210


Cost of whitewashing 550 m2 CSA of the conical tomb

= (210 x 550)/100= Rs 1155



CSA of 1 cap

= πrl

= (22/7) x 7 x 24

= 22 x 24

= 528 m2




Area of the sheet required to make 10 such conical caps

= 10 x 528

= 5280 m2



r= 20 cm = 0.20 m

h= 1 m


l2=h2+r 2  

l2=12+0.20 2  

l2= 1+ 0.04

l2=1.04

l=1.02


CSA of 50 hollow cones 

= 50 x πrl

= 50 x (22/7) x 0.20 x 1.02

= 3.14 x 50 x 0.20 x 1.02

= 32.028 m2


Cost of painting 1 m2 CSA of the hollow cone

= Rs 12  


Cost of painting 32.028 m2 CSA of the hollow cone

= Rs 12  x 32.028

= 384.336 m2 = 384.34 m2