A cylinder shaped sculpture is 24 meters high with a diameter of 6.8 meters. An artist plans to spray paint the entire surface with silver paint. If 1 can of spray paint covers 50 square meters, how many cans does the artist need to paint the sculpture?
Area of circle = πr^2
Perimeter of a circle = 2πr
Diameter = 2r
Paint needed = (2πr^2 + 24[2πr])/50
I'll let you do the calculations.
5 Cans
SA=2B+PH
SA=2(pi*r^2)+(2*pi*r)H
SA=2(3.14*3.4^2)+(2*3.14*3.4)8
SA=2*36.2984+21.352*8
SA=72.5968+170.816
SA=243.4128 ft^2
5 Cans
SA=2B+PH
SA=2(pi*r^2)+(2*pi*r)H
SA=2(3.14*3.4^2)+(2*3.14*3.4)8
SA=2*36.2984+21.352*8
SA=72.5968+170.816
SA=243.4128 ft^2
CANS=243.4128/50=5 cans
14
To find out how many cans of spray paint the artist needs to paint the sculpture, we need to find the surface area of the cylinder.
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr² + 2πrh,
where r is the radius and h is the height of the cylinder.
First, let's calculate the radius of the cylinder. The diameter is given as 6.8 meters, so the radius (r) can be calculated by dividing the diameter by 2:
r = 6.8 / 2 = 3.4 meters.
Next, we can calculate the surface area of the cylinder using the given height (h) and the calculated radius (r):
Surface Area = 2π(3.4)² + 2π(3.4)(24).
Surface Area = 2π(11.56) + 2π(81.6).
Surface Area = 23.12π + 163.2π.
Surface Area = 186.32π square meters.
Now, we know that 1 can of spray paint covers 50 square meters. To find out how many cans the artist needs, we can divide the total surface area of the cylinder by the coverage of one can:
Number of cans = Surface Area / Coverage per can.
Number of cans = 186.32π / 50.
Number of cans ≈ 11.81 cans.
Since we can't have a fraction of a can, the artist would need to round up to the nearest whole number. Therefore, the artist needs 12 cans of spray paint to cover the entire surface of the cylinder.