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lord [1]
3 years ago
6

A manufacturer states their paint will cover 400 square feet per gallon. How much paint should you purchase to paint a house tha

t is 30 feet wide and 54 feet long and has siding 10 feet high?
Mathematics
1 answer:
sdas [7]3 years ago
7 0


u need to find surface area which is 2(lw)+2(lh)+2(wh)

so is 2(30x54)+2(30x10)+2(54x10)= 2(1620)+2(300)+2(540)=

3240+600+1080=4920 square feet

divide the amount u need by the amount per gallon so is 4920/400 which is 12.3 gallons

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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)

<em>step 1</em>

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

<em>step 2</em>

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

<em>Find the area of the larger circle</em>

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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3 years ago
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