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14.
Case Study - 2 John planned a birthday party for his younger sister with his friends.
ded 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 : Cake : Cylindrical shape with diameter 24 cm and height 14 cm. cap: Conical shape with base circumference 44 cm and height 24 cm.
2
Based on the above information, answer the following questions: (a) How many square cm paper would be used to make 4 such caps ?
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 cm3 equals 100 g of cake?
-30/3/1

Sagot :

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a. The number of square cm of paper that would be used to make 4 caps is 3154.56 cm².

b. For the cake to have the required dimensions, they should order 1 kg of cake.

a.

The number of square cm of paper that would be used to make 4 caps is 3154.56 cm².

To find the number of square cm paper would be used to make 4 caps, we need to find the area of a cone.

Area of a cone

The area of a cone, A = πr² + πr[√(h² + r²)] where

  • r = radius of cone and
  • h = height of cone

Now given that the base circumference of the cone is C = 44 cm. So,

C = 2πr where r = radius of base

So, r = C/2π = 44 cm/2π = 22 cm/3.142 = 7 cm

The height of the cone, h = 24 cm

So, A = πr² + πr[√(h² + r²)]

A = π(7 cm)² + π(7 cm)[√((24 cm)² + (7 cm)²)]

A = π(7 cm)² + π(7 cm)(7)[√((4 cm)² + (1 cm)²)]

A = 49π cm² + 49π cm[√(16 cm² + 1 cm²)]

A = 49π cm² + 49π cm[√(17 cm²)]

A = 49π [1 cm² + 4.123 cm²)]

A = 49π [5.123 cm²)]

A = 251.032π

A = 788.64 cm²

Since the area of one cap is A = 788.64 cm²,

the area of 4 caps is A' = 4A

= 4 × 788.64 cm²

= 3154.56 cm²

So, the number of square cm of paper that would be used to make 4 caps is 3154.56 cm².

b.

For the cake to have the required dimensions, they should order 1 kg of cake.

To find the amount of cake to be ordered, we need to find the volume of a cake since it is the volume of a cylinder.

Volume of a cylinder

The volume of a cylinder is V = πd²h/4 where

  • d = diameter of cake = 24 cm and
  • h = height of cake = 14 cm

Substituting the values of the variables into the equation, we have

V = πd²h/4

V = π(24 cm)²(14 cm)/4

V = π(576 cm)²(14 cm)/4

V = 8064π cm³/4

V = 2016π cm³

V = 6333.45 cm³

So the volume of the cake is 6333.45 cm³

Since 650 cm³ equals 100 g, 6333.45 cm³ = 6333.45 cm³ × 100 g/650 cm =  974.4 g = 0.974 kg ≅ 1 kg.

So, for the cake to have the required dimensions, they should order 1 kg of cake.

Learn more about volume of a cake here:

https://brainly.com/question/27570775

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