Question

9. A joker having a cone-shaped cap of base radius
10.5 cm, decides to change the colour of his cap.
He buys three different colours of volumes in the
ratio 1:2:3. He mixes the three colours and paints
uniformly on the outer surface of the cap by using
the whole mixture without the loss of generality of
volume conservation. The slant height of the cap
is half the circumference. The sum of volumes of
the three colours is 54.45 cm.
(i) What is the thickness of the paint on the cap?
(ii) What are the volumes of the colours bought
by the joker?
(iii) Which mathematical concept(s) is (are) used
in the above problem?
(iv) Which qualities does the joker have?
[Value Based Question] (4)​

Answer 1

Answer⤵️⤵️

Given

r=7 cm

h=24 m

Let slant height be

′

l

′

We know l 2 =h 2 +r 2 l 2 =24 2 +7 2l 2 =576+49l 2 =625l=25 cm

Curved surface area of 1 jokers cap =πrl

= 72 ×7×25

=22×25

=550 cm 2

So,

Curved surface area of 10 jokers cap =10×550

=5500 cm2