Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
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
#SPJ1
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.