John planned a birthday party for his younger sister with his friends. They decided to make some birthday caps by themselves and to buy a cake from a bakery shop. For these two items, they decided the following dimensions :

Question

Cake : Cylindrical shape with diameter 24 cm and height 14 cm.
Cap: Conical shape with base circumference 44 cm and height 24 cm. Based on the above information, answer the following questions :
(a) How many square cm paper would be used to make 4 such caps ?
(b)The bakery shop sells cakes by weight (0.5 kg, 1 kg, 1.5 kg, etc.). To have the required dimensions, how much cake should they order, if 650 cm^3 equals 100 g of cake?

Answer 1

cap: area = πrs
where r = 44/(2π) and s^2 = r^2 + h^2

cake: v = πr^2 h cm^3
weight = v * 100g/650cm^3 * 1kg/1000g