Question

1. A baker is making a cake. the top layer of the cake has a diameter of 12 inches, and the bottom layer has a diameter of 36 inches. How big should the middle layer of the cake be?

2. The perimeter of the kite is 75cm. The length of its side is 17 cm more than half the length of the other. Find the length of each side of the kite

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Answer 1

Answer:

1. 9 inches

Step-by-step explanation:

1. The diameter of the topmost layer of the cake = 6 inches

And the bottom layer = 12 inches

Diameter of middle layer will be the average of top and bottom layers diameter.

Diameter of middle layer = (6+12)/2

Or, Diameter of middle layer = 18/2

Or, Diameter of middle layer = 9 inches

Therefore, the diameter of middle layer = 9 inches

Answer 2

The given value of the top and bottom diameters of the cake and the

expression of the sides of the kite gives the following values.

1. The diameter of the middle layer should be 24 inches

2. The length of the sides of the kite are $\underline{13.\overline 6 \ cm}$ and $\underline{ 23\frac{5}{6} \ cm}$

How can the size of the cake and dimension be found?

Given:

The diameter of the top layer = 12 inches

The diameter of the bottom layer = 36 inches

Required:

The size of the middle layer.

Solution:

An equal increment of each layer can be found follows;

$Increment \ of \ each \ layer = \dfrac{36 - 12}{2} = \mathbf{ 12}$

Equal increment of each layer is therefore 12 inches per layer

The diameter of the middle layer is therefore;

Diameter of top layer + 12 inches = 12 inches + 12 inches = 24 inches

• The diameter of the middle layer should be 24 inches

2. The given parameters are;

The perimeter of a kite = 75 cm

The length of the a side = 17 + $\mathbf{\frac{1}{2}}$× The length of the other side

Required:

The lengths of each side of the kite

Solution:

A regular kite has four sides, two of which have the same length.

Let x represent the length of one side of the kite, we have;

The length of the other side with different length = 17 + $\frac{1}{2}$ × x

The perimeter of the kite is therefore;

(x + x) + (17 + $\mathbf{\frac{1}{2} }$ × x + 17 + $\mathbf{\frac{1}{2}}$ × x) = 75

Which gives;

3·x + 2 × 17 = 3·x + 34 = 75

3·x = 75 - 34 = 41

x = 41 ÷ 3 = $13.\overline 6$

The length of a side of the kite, x = $\mathbf{13.\overline 6 \, cm}$

The length of the other side of a kite = 17 + $\frac{1}{2}$ × x

Which gives;

The length of the other side of the kite = 17 +  $\frac{1}{2}$ × $13.\overline 6$ = 23$\frac{5}{6}$

The length of the other side of the kite = $\mathbf{ 23\frac{5}{6} \ cm}$

The lengths of the sides of the kite are; $\underline{13.\overline 6 \, cm}$ and  $\underline{ 23\frac{5}{6} \ cm}$

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