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2 years ago

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Cindy is baking a 2-layer cake. The top layer has a diameter of 8 inches and the bottom layer has a diameter of 10 inches. What

is the difference in area between the top surfaces of the two cakes? Use 3. 14 for π

1 answer:

Alenkinab [10]2 years ago

5 0

The difference in area between the top surfaces of the two cakes is 28.26 inches²

<h3>Area of a circle</h3>

area = πr²

where

r = radius

Therefore,

area of top layer = πr²

d = 2r

r = d / 2

r = 8 / 2

r = 4 inches

area of top layer = 3.14 × 4²

area of top layer = 3.14 × 16

area of top layer = 50.24 inches²

area of the bottom layer = πr²

r = 10 / 2 = 5 inches

area of the bottom layer = 3.14 × 5²

area of the bottom layer = 3.14 ×25

area of the bottom layer = 78.5 inches²

Difference in area between the top surfaces of the two cakes can be found as follows:

78.5 - 50.24 = 28.26 inches²

learn more on circle here: brainly.com/question/10264279

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$x_{1,2} = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$ ......[1]

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$x_{1,2} = \frac{-10\pm \sqrt{10^2-4\cdot 3 \cdot c}}{2 \cdot 3}$

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Here,

$x_1 = \frac{-10 + \sqrt{100- 12c}}{6}$ , ......[2]

$x_2= \frac{-10 - \sqrt{100- 12c}}{6}$ .....[3]

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$x_1 = \frac{-10 + \sqrt{100- 12\cdot 8}}{6}$

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$x_1 = \frac{-10 + \sqrt{4}}{6}$

Simplify:

$x_1 = \frac{-4}{3}$

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$x_2 = \frac{-10 - \sqrt{100- 12\cdot 8}}{6}$

or

$x_2 = \frac{-10 - \sqrt{100- 96}}{6}$ or

$x_2 = \frac{-10 - \sqrt{4}}{6}$

Simplify:

$x_2 = -2$

therefore, the solution for the given equation is: $-\frac{4}{3}$ and -2.

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