SOLUTION: The radius and height of a rught circular cone are 21 n 28cm. From its base to a height of 14 cm the portion of the curved surface was painted golden and the upper portiob as silve

Question 981752: The radius and height of a rught circular cone are 21 n 28cm. From its base to a height of 14 cm the portion of the curved surface was painted golden and the upper portiob as silver. Find the total cost of painting the whole curved surface at the rate of Rs50 /cm^2 for the golden colour and at the rate of Rs 40/cm^2 fir the silver colour.
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The radius and height of a rught circular cone are 21 n 28cm. From its base to a height of 14 cm the portion of the curved surface was painted golden and the upper portiob as silver. Find the total cost of painting the whole curved surface at the rate of Rs50 /cm^2 for the golden colour and at the rate of Rs 40/cm^2 fir the silver colour.
The radius circular cone is 21
and height of a 28cm.
From its base to a height of 14 cm
The lower part is a frustum of a cone

.

Triangle AME and ANC are similar ( A A test of similarity)
14/28 = r1/21
r1= 10.5
By Pythagoras theorem AC^2 = AN^2 +NC^2
=28^2 +21^2
=1225
AC=35
Again
AM/AN = AE/AC
1/2 = AE/AC
1/2 = AE/35
AE = 17.5
The bottom portion is a frustum of cone
Curved surface area of frustum = pi*(r1+r2)*l=pi*(21+10.5)*17.5
=1732.5 cm^2
Multiply by cost Rs. 50/cm^2
= Rs. 86625
the curved surface of upper portion= pi*r*l
pi*10.5 * 17.5
= 577.26 cm^2
multiply by 40
=Rs 23,090.70
Add up both costs

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