can any one help on this question?

Question

If 1 gallon of paint covers 400 square feet about how many gallons of paint are needed to paint the outside of a spherical tank of diameter 20 feet?

Answer 1

Surface Area of a sphere is
4(pi)(r^2)

So... the SA of your spherical tank is
4(pi)(10^2) = 400(pi)

Divide that by 400....

You'll need (pi) gallons of paint = 3.1415...

Answer 2

Hey there,

1) Find the surface area of the spherical tank first.

Surface area of a sphere = 4(pi)r^2

Diameter = 20ft, so
Radius = r = 10ft

Now substitute 10ft into your first equation

Surface area of the sphere
= 4(pi)(10)^2
= 4(pi)(100)
= 400(pi)
= 1257.143 square feet

You know that 1 gallon of paint can cover 400 square feet, so -

2) Divide the surface area of the spherical tank by 400 square feet to find out how much paint is needed.

1257.143/400
= 3.1428 gallons of paint.

But you'll need to buy 4 gallons, if that's what your teacher's looking for.

Hope this helps! :o)

Answer 3

This is quite an easy one luckily.
We are told that 1 gallon of paint covers a surface area (S.A.) of 400 sq ft.
We need to know what S.A. we have to cover.
In order to do this, we need to know the formula for calculating the S.A. of a sphere (since we are told that the tank is spherical).
The S.A of a sphere is given by the general formula S.A = 4 x pi x r x r (read as 4 pi r squared).
In our case, we are told that the diameter of the sphere is 20 ft.
Since this is = to double the radius implies inversely that the radius = half the diameter, thus radius = 10 ft
Therefore, substituting in 10 for r we get:
S.A.= 4 x pi x 10 x10 = 4 x pi x 100 sq ft (remember units)
S.A = 1256.64 sq ft approx.
We need to know the number of gallons of paint to be used, however.
No. of gallons required= S.A. of spherical tank DIVIDED BY Coverage area per gallon
No. of gallons required = 1256.64 sq ft/ 400 sq ft
No. of gallons required = 3.14 (or pi as an exact answer)gallons.
Rounded up to the nearest gallon implies FOUR GALLONS would need to be available to account for any errors in painting etc....

Answer 4

Vol (sphere) = 4/3 * pi * r^3
Area (sphere) = 4 * pi * r^2

r = d/2 = 10 ft

Area = 4 * pi * 100 = 400 * pi sqft

gallons needed = Area * 1gal/400 sqft
= 400 * pi / 400 = pi gallons or 3.14 gallons

So you need -about- 3 gallons, but if you want a more accurate answer, you will actually need to buy 4 gallons to cover it completely.

Answer 5

The surface area of a sphere is 4(pi)r^2

The diameter is 20 feet, the radius is therefore 10 feet.
The surface area of the sphere is therefore: 4(pi)100 = 1256.637 ft^2.

1gallon of paint per 400 ft^2

(1gal/400ft^2)(1256.637ft^2) units cancel = 3.14159 gallons.

Answer 6

Area of the sphere = 4 * Pi * r^2
= 4 * Pi * 10 * 10
= 400 * Pi square feet.

So you need Pi gallons, or roughly 3.1416 gallons.

Answer 7

Area of sphere = 4 pi r^2

sphere = 4 pi 10^2 = 1256.6 sq ft

1256.6 / 400 = 3.14 gal of paint

Answer 8

Surface area of a sphere is 4πr², so
SA = 4(3.1416)(10)² = 1256.6 ft²

divide that by 400 ft²/gal and get 3.1416 gal. of paint. You'll need to buy 4 gal to do the job.