Johnny wants to ship a package to his friend a shipping company charges 2.49 for the first pound and 1.24 for each additional po
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Answer:
Approximately 313 cakes of similar size as those 50 cut from the smaller cake, can be cut from the bigger cake.
Step-by-step explanation:
The complete question is with the missing image of the cakes is attached to this solution.
From the image provided, the dimensions of the smaller cake = 2 ft × 1.6 ft
The dimensions of the larger cake = 5 ft × 4 ft
50 cakes are obtained from the smaller cake, how many cakes can be obtained from the bigger cake?
Area of the smaller cake = 2 × 1.6 = 3.2 ft²
Area of the bigger cake = 5 × 4 = 20 ft²
3.2 ft² cake provides 50 cakes.
20 ft² cake will provide (20×50/3.2) cakes = 312.5 cakes
Rounded to the nearest piece of cake = 313 cakes
Hope this Helps!!!
The image provided is the shape of a triangular prism.
The base of the prism (triangles) are both equilateral. This means that all sides measure 3 centimeters.
Find the area of one triangle based on the information given:
A = 1/2bh
**Notice that we cannot put in any number for the height of the triangular base because we are only given three side. As a result, we have to take a different approach to finding the area of the triangles. We can use another method known as Heron's Formula.**
You can use this formula to find the area of a triangle using the 3 side lengths.
Heron's Formula :
1) First, find the semi-perimeter of the triangle. We can find this by adding all the sides and dividing the sum by 2.
= 3 + 3 + 3 / 2
= 4.5
Use this formula to find the area:
A = √S(S - A)(S - B)(S - C)
**S, in this case, represents the semi-perimeter.**
Substitute the side lengths of the triangle and semi-perimeter.
A = √4.5(4.5 - 3)(4.5 - 3)(4.5 - 3)
A = √4.5(1.5)(1.5)(1.5)
A = √15.1875
Then, we simplify the number by turning the decimal into a fraction and further reducing it.
We would get:
A = √243 / √16
Simplify √16 into 4 and simplify the radical √243 into 9√3 / 4.
Now, multiply this number by two because we have another triangular base.
A = 9√3 / 4 × 2
A = 9√3 / 2 or 7.79422863406
2) Now that we have the surface areas of both triangles, we can find the surface areas of the rectangles.
This is easier to find because the triangles are equilateral and the height of the prism is simply 15.
A = lw
A = (15)(3)
A = 45
45 is the area of one rectangle. Since there are 3, multiply 45 by 3.
A = 45 × 3
A = 135
3) Add up all your values to find the surface area.
S.A. = 135 + 7.79422863406
S.A. = 142.794228634 cm²
Solution : 142.794228634 cm²
The base of the prism (triangles) are both equilateral. This means that all sides measure 3 centimeters.
Find the area of one triangle based on the information given:
A = 1/2bh
**Notice that we cannot put in any number for the height of the triangular base because we are only given three side. As a result, we have to take a different approach to finding the area of the triangles. We can use another method known as Heron's Formula.**
You can use this formula to find the area of a triangle using the 3 side lengths.
Heron's Formula :
1) First, find the semi-perimeter of the triangle. We can find this by adding all the sides and dividing the sum by 2.
= 3 + 3 + 3 / 2
= 4.5
Use this formula to find the area:
A = √S(S - A)(S - B)(S - C)
**S, in this case, represents the semi-perimeter.**
Substitute the side lengths of the triangle and semi-perimeter.
A = √4.5(4.5 - 3)(4.5 - 3)(4.5 - 3)
A = √4.5(1.5)(1.5)(1.5)
A = √15.1875
Then, we simplify the number by turning the decimal into a fraction and further reducing it.
We would get:
A = √243 / √16
Simplify √16 into 4 and simplify the radical √243 into 9√3 / 4.
Now, multiply this number by two because we have another triangular base.
A = 9√3 / 4 × 2
A = 9√3 / 2 or 7.79422863406
2) Now that we have the surface areas of both triangles, we can find the surface areas of the rectangles.
This is easier to find because the triangles are equilateral and the height of the prism is simply 15.
A = lw
A = (15)(3)
A = 45
45 is the area of one rectangle. Since there are 3, multiply 45 by 3.
A = 45 × 3
A = 135
3) Add up all your values to find the surface area.
S.A. = 135 + 7.79422863406
S.A. = 142.794228634 cm²
Solution : 142.794228634 cm²