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.
The area of a cone, A = πr² + πr[√(h² + r²)] where
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.
The volume of a cylinder is V = πd²h/4 where
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:
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