How do I solve these?
Which paint roller can you spread more paint on the wall in one revolution? A cylinder with a 2 inch diameter and 11 inch height or a cylinder with a 3 inch diameter and 7 inch height? What are the volumes and surface areas for both rollers?
2007-01-18 20:09:38 · 4 answers · asked by Emily A 1 in Science & Mathematics ➔ Mathematics
cylinder with a 2 inch diameter and 11inch height spreads more paint in one revolution!
Surface area of cylinder = 2*π*r*(r+h)
r is the radius
h is the height
But surface area available for rolling = 2*π*r*h
Surface area (for rolling) I st cylindrical roller = 2*π*1*11
= 22*π sq inches
Surface area (for rolling) IInd cylindrical roller = 2*π*1.5*7
= 21*π sq inches
Volume of a cylinder = π*r²*h
Volume of I st cylindrical roller = π*1²*11 = 11*π inches^3
Volume of II nd cylindrical roller = π*1.5²*7 = 15.75*π inches^3
2007-01-18 20:15:47 · answer #1 · answered by Som™ 6 · 1⤊ 0⤋
the cylinder with 2 inch diameter has a circumference of 2Pi inches and its outer surface is 2pi*11= 22*pi inches ^2= 69.12nches ^2
the cylinder with 3 inch diameter has a circumference of 3Pi inches and its outer surface is 3pi*7= 21*pi inches ^2= 65.88inches ^2
So ,the first is slightly better
the volume is given by formula V = pi *r^2 *h
For the first r= d/2 =1 inch V = pi *1*11 = 11pi(34.6) inches^3
for the second r =1.5 so V = pi *1.5^2 *7 = 33 inches^3
2007-01-19 05:02:25 · answer #2 · answered by maussy 7 · 0⤊ 0⤋
11*2Ï > 7*3Ï, which are the respective effective surface areas (areas of ends not included)
The volumes are:
11(4/4)Ï = 11Ï and 63Ï/4
2007-01-19 04:37:02 · answer #3 · answered by Helmut 7 · 1⤊ 0⤋
S = pi d h and V =pi d^2 h /4.
2007-01-19 04:13:27 · answer #4 · answered by gianlino 7 · 1⤊ 1⤋