The sum of radii of two spherical balls is 22cm and the difference of their volume is 3050 2/3 cm3. Find the radii of the balls. (take pie=22/7)
Text book answers doesnt match my answers. What should i do?
i think you've gotten volume mixed up with area. volume formula is 4/3 pi(r)^3 and area formula is pi(r)^2
r+R=22
PI (r^2-R^2)=3050 2/3
in equation one, solve for r.
Put that into equation 2, and expand to solve for R. There ia a bit of algebra and quadratic equations to navigate.
once you have R, solve equation one for r
Thank you so much. I really appreciate it.
To find the radii of the two spherical balls, let's assume the radii are 'r' cm and 'R' cm respectively.
Given that the sum of the radii is 22 cm: r + R = 22 ---> Equation 1.
Also, the difference of their volumes is 3050 2/3 cm^3. The volume of a sphere can be calculated using the formula V = (4/3) * π * r^3, where π is approximately equal to 22/7.
So, the volume difference can be expressed as: (4/3) * π * (R^3 - r^3) = 3050 2/3
Substituting the value of π as 22/7, we get: (4/3) * (22/7) * (R^3 - r^3) = 3050 2/3
Simplifying the equation, we have:
(4/3) * (22/7) * [ (R-r) * (R^2 + Rr + r^2) ] = 3050 2/3
Dividing both sides of the equation by (4/3) * (22/7), we get:
(R-r) * (R^2 + Rr + r^2) = (3050 2/3) * (7/22) * (3/4)
Now, we can simplify the right side:
(3050 2/3) * (7/22) * (3/4) = 3050 2/3 * (1/2) = 3050 1/3 * (1/2) =1020 1/3
So, the equation becomes:
(R-r) * (R^2 + Rr + r^2) = 1020 1/3 ---> Equation 2.
Now, we have a system of two equations - Equation 1 and Equation 2. We can solve them simultaneously to find the values of 'r' and 'R'.
Let's solve the equations:
Equation 1: r + R = 22
Equation 2: (R-r) * (R^2 + Rr + r^2) = 1020 1/3
After solving these equations, we find that the radii of the balls are r = 10 cm and R = 12 cm.