Question

A cake has a circumference of 25 1/7inches. What is the area of the cake? Use 22/7 to approximate π. Round to the nearest hundredth. Enter your answer in the box.

Answer 1

The area of the cake is 50.29 square inches.

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Let's understand a few concepts:

To calculate the area of the cake we will use the following formulas:

• To find the radius of the cake → $\boxed{\bold{Circumference \:of\:a\:circle = 2\pi r}}$

• To find the area of the cake → $\boxed{\bold{Area \:of\:a\:circle = \pi r^2}}$

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Let's solve the given problem:

The circumference of the cake = $25\frac{1}{7} \:inches = \frac{(25\times 7) + 1}{7} \:inches = \frac{176}{7} \:inches$

Let "r" inch be the radius of the cake.

Therefore, by using the formula of circumference we can form an equation as,

$2\pi r=\frac{176}{7}$

$\implies 2 \times \frac{22}{7} \times r = \frac{176}{7}$

$\implies 2 \times 22 \times r =176$

$\implies 44 \times r =176$

$\implies r =\frac{176}{44}$

$\implies r =4\:inch$

Now, by using the formula for the area of a circle, we get

The area of the cake is,

= $\pi r^2$

= $\frac{22}{7} \times 4^2$

= $\frac{22}{7} \times 16$

= $50.28571429\:sq. \:inch$

as asked in the question we will now round off the answer to its nearest hundredth

= $\bold{50.29\:square \:inches}$

Thus, the area of the cake is 50.29 square inches.

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Answer 2

Answer:

50.29 Square inches

Step-by-step explanation:

The area of the cake is 50.29 square inches.

-------------------------------------------------------------------------------------

Let's understand a few concepts:

To calculate the area of the cake we will use the following formulas:

To find the radius of the cake → \boxed{\bold{Circumference \:of\:a\:circle = 2\pi r}}

Circumferenceofacircle=2πr

To find the area of the cake → \boxed{\bold{Area \:of\:a\:circle = \pi r^2}}

Areaofacircle=πr

2

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Let's solve the given problem:

The circumference of the cake = 25\frac{1}{7} \:inches = \frac{(25\times 7) + 1}{7} \:inches = \frac{176}{7} \:inches25

7

1

inches=

7

(25×7)+1

inches=

7

176

inches

Let "r" inch be the radius of the cake.

Therefore, by using the formula of circumference we can form an equation as,

2\pi r=\frac{176}{7}2πr=

7

176

\implies 2 \times \frac{22}{7} \times r = \frac{176}{7}⟹2×

7

22

×r=

7

176

\implies 2 \times 22 \times r =176⟹2×22×r=176

\implies 44 \times r =176⟹44×r=176

\implies r =\frac{176}{44}⟹r=

44

176

\implies r =4\:inch⟹r=4inch

Now, by using the formula for the area of a circle, we get

The area of the cake is,

= \pi r^2πr

2

= \frac{22}{7} \times 4^2

7

22

×4

2

= \frac{22}{7} \times 16

7

22

×16

= 50.28571429\:sq. \:inch50.28571429sq.inch

as asked in the question we will now round off the answer to its nearest hundredth

= \bold{50.29\:square \:inches}50.29squareinches

Thus, the area of the cake is 50.29 square inches.

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