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3 years ago

Find the area of the ring-the shaded region

Mathematics

1 answer:

Vilka [71]3 years ago

8 0

The area of the (ring) - the shaded region is 75.36 in²

Solution:

The value of π = 3.14

Radius of the inner circle = 5 in

Area of the inner circle = πr²

= π × 5²

Area of the inner circle = 25π

Radius of the outer circle = (5 + 2) = 7 in

Area of the outer circle = πr²

= π × 7²

Area of the outer circle = 49π

Area of the shaded ring = Area of the outer circle – Area of the inner circle

= 49π – 25π

= 24π

= 24 × 3.14

= 75.36 in²

The area of the (ring) - the shaded region is 75.36 in².

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35 POINTS AVAILABLE

aliina [53]

Answer:

Part 1) The length of each side of square AQUA is $3.54\ cm$

Part 2) The area of the shaded region is $(486\pi-648)\ units^{2}$

Step-by-step explanation:

Part 1)

step 1

Find the radius of the circle S

The area of the circle is equal to

$A=\pi r^{2}$

we have

$A=25\pi\ cm^{2}$

substitute in the formula and solve for r

$25\pi=\pi r^{2}$

simplify

$25=r^{2}$

$r=5\ cm$

step 2

Find the length of each side of square SQUA

In the square SQUA

we have that

SQ=QU=UA=AS

$SU=r=5\ cm$

Let

x------> the length side of the square

Applying the Pythagoras Theorem

$5^{2}=x^{2} +x^{2}$

$5^{2}=2x^{2}$

$x^{2}=\frac{25}{2}\\ \\x=\sqrt{\frac{25}{2}}\ cm\\ \\ x=3.54\ cm$

Part 2) we know that

The area of the shaded region is equal to the area of the larger circle minus the area of the square plus the area of the smaller circle

Find the area of the larger circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=AB=18\ units$

substitute in the formula

$A=\pi (18)^{2}=324\pi\ units^{2}$

step 2

Find the length of each side of square BCDE

we have that

$AB=18\ units$

The diagonal DB is equal to

$DB=(2)18=36\ units$

Let

x------> the length side of the square BCDE

Applying the Pythagoras Theorem

$36^{2}=x^{2} +x^{2}$

$1,296=2x^{2}$

$648=x^{2}$

$x=\sqrt{648}\ units$

step 3

Find the area of the square BCDE

The area of the square is

$A=(\sqrt{648})^{2}=648\ units^{2}$

step 4

Find the area of the smaller circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=(\sqrt{648})/2\ units$

substitute in the formula

$A=\pi ((\sqrt{648})/2)^{2}=162\pi\ units^{2}$

step 5

Find the area of the shaded region

$324\pi\ units^{2}-648\ units^{2}+162\pi\ units^{2}=(486\pi-648)\ units^{2}$

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Answer:

-1/10

Step-by-step explanation:

We need to get a common denominator of 10

-1/2 *5/5 = -5/10

2/5*2/2 = 4/10

-5/10 +4/10 = -1/10

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lys-0071 [83]

For this case we must find 35% of 280.

Kerrie gets 10% and then 25%. So:

10% of 280:

280 ------------> 100%

x -----------------> 10%

Where "x" represents the amount given by 10% of 280.

$x = \frac {10 * 280} {100}\\x = 28$

Thus, 10% of 280 is 28.

Now, we find 25% of 280:

280 ------------> 100%

x -----------------> 25%

Where "x" represents the amount given by 25% of 280.

$x = \frac {25 * 280} {100}\\x = 70$

Thus, 25% of 280 is 70.

So we have that 35% of 280 is given by:

$28 + 70 = 98$

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Answer:

Option A

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