a cylinder has a height of 7cm and a surface area S=88meter square. what are the radius and volume of this cylinder?convert your answer into cm.
V = pi r^2 h
S = 2 pi r^2 + 2 pi r h
= 88 * 10^4 cm^2
so
2 pi (r^2 + 7r) = 88 *10^4
r^2 + 7 r = about 14 *10^4
r is around 400 (do quadratic with calculator)cm
almost all of the area is in the top and bottom so V = about 7*44*10^4
To find the radius and volume of the cylinder, we can use the surface area formula and the volume formula for a cylinder.
1. First, let's find the radius.
The formula for the surface area of a cylinder is:
S = 2πrh + 2πr^2
where S is the surface area, r is the radius, and h is the height of the cylinder.
We are given that the surface area is S = 88 square meters, and the height is h = 7 cm. However, we need to convert the surface area from square meters to square centimeters.
1 square meter = 10000 square centimeters,
so 88 square meters = 88 * 10000 = 880000 square centimeters.
Substituting these values into the formula, we get:
880000 = 2πr * 7 + 2πr^2
Simplifying the equation, we have:
880000 = 14πr + 2πr^2
Rearranging the equation, we get:
2πr^2 + 14πr - 880000 = 0
To solve this quadratic equation, we can either use factoring, completing the square, or the quadratic formula. However, in this case, it is more efficient to use an online solver or calculator to find the approximate value of r.
2. Once you have found the radius r, you can calculate the volume of the cylinder.
The formula for the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Substituting the values we have, the volume becomes:
V = π * (r)^2 * 7
Calculate this expression using the value of r you found in Step 1 to obtain the volume in cubic centimeters.
Remember to convert your answer to cm by using appropriate conversion factors if necessary.