Ms. Aarushi got the prize in an essay writing competition for which her father
bought her favourite huge raspberry ice cream waffle cone. The ice cream
cone has a radius of 7 cm and a height of 24 cm. The spherical ice cream
sits on the cone such that half the ice cream is inside the cone She observed
the shadow of the ice cream on the wall. It was as shown in the given figure.
1
(i) Find the volume (approx. in litres) of the raspberry ice cream placed on the waffle cone.
(a) 1.232 litres (b) 1.437 litres
(c) 0.718 litres (d) 2.702 litres
(ii) The waffle cone is coated with chocolate syrup on the outside of the cone. Find the cost of covering the
waffle cone, if 1 littre of chocolate syrup covering an area of 1000 sq.cm costs Rs. 60.
1
(a) Rs.45
(b) Rs. 52
(c) Rs. 33
(d) Rs. 42.24
(iii) Find the area of the shadow seen by Ms. Aarushi on the wall.
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(a)
252 sq.cm
(b)
329 sq. cm
(C)
245 sq. cm (d) 322 sq. cm
(iv) What should be the height of the cone, if the ice cream inside the cone fills it completely?
1
(a) 7 cm
(b) 14 cm
(c)
The ice cream cone costed her Rs 150. What would its price, if the visible surface of the ice cream
(d) 24 cm
(v)
were covered with caramel at the rate of Rs.0.03 per sq. cm.
(a) Rs. 193.12
(b) Rs. 214.68
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(c) Rs.21.56 (d) Rs. 171.56
Solution :–
→ Radius of cone = 7cm = Radius of spherical raspberry ice cream .
so,
→ Volume = (4/3)πr³ = (4/3) * (22/7) * (7)³ = 1437.34 cm³ .
we know that,
then,
→ Volume = 1437.34/1000 = 1.437 litres (b) (Ans.1)
now,
→ CSA of conical part = πrl = (22/7) * 7 * √(7² + 24²) = 22 * 25 = 550 cm².
then,
→ 1000 cm² cost = Rs.60
→ 550 cm² cost = (60/1000) * 550 = Rs.33 (c) (Ans.2)
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