Question

A model of a rectangular stove top with four circular burners is shown. The side lengths of the stove top and the diameters of the burners are labeled.
Which measurement is the best estimate of the area in square inches of the stove top that does not include the area of the burners?
A) 108 in.2
B) 492 in.2
C) 420 in.2
D) 528 in.2

Answer 1

Answer:

C) 420 in^2

Step-by-step explanation:

The stove top has a rectangular shape, so its total area is given by:

$A=Lw$

where

L = 24 in is the length of the stove top

w = 22 in is the width of the stove top

However, here we have to subtract the area of the 4 circular burners. The area of each circular burner is given by

$A'=\pi r^2$

where r is the radius of each burner. Since the diameter is 6 inches, the radius is half that value, so

r = 3 in

Therefore we can write the net area of the stove top that does not include the area of the burners as

$A_{net} = A-4A'$

And substituting, we find

$A_{net}=Lw-4\pi r^2=(24)(22)-4\pi (3)^2=415 in^2$

So the closest estimate is

C) 420 in^2

Answer 2

The best estimate of the area in square inches of the stovetop that does not include the area of the burners is 420 square inches and it can be determined by using formula of rectangular shape.

Given that,

A model of a rectangular stovetop with four circular burners is shown.

The side lengths of the stovetop and the diameters of the burners are labeled.

We have to determine,

Which measurement is the best estimate of the area in square inches of the stovetop that does not include the area of the burners?

According to the question,

The length of the stovetop is 24 inches,

And the width of the stovetop is 20 inches.

In this problem the measurement of the area is in two part as given in the figure. firstly we have to find the of the rectangular stove then the area of the of the circular burners after subtraction the area of circular burners.

The area of the given rectangular shape is given by,

$\rm Area = length \times width$

The area of the given rectangular shape is,

$\rm Area = length \times width\\\\\rm Area = 22\times 24\\\\\rm Area = 528 \ inches^2$

And the area of the circular burners is given by,

$\rm Area = \pi r^2$

Where r is the radius of the circular burners.

The area of the circular burners is given by,

$\rm Area = 4\pi r^2\\\\Area = 4\pi (3)^2\\\\Area = 36 \times 3.14\\\\Area = 113\ inches^2$

Therefore,

The best estimate of the area in square inches of the stovetop that does not include the area of the burners is determined by subtracting the area of circular burners from the area of the stovetop.

$\rm Area = 528-113\\\\Area = 415 \ inches^2$

Hence, The best estimate of the area in square inches of the stovetop that does not include the area of the burners is 420 square inches.

To know more about Area of Circle click the link given below.

https://brainly.com/question/1238286