Explanation :
Let's assume the radius of the cylinder and cone to be r cm, and the height of the cone to be h cm.
The surface area of the cylinder can be calculated as follows:
Surface area of the cylinder = 2πrh
Given that the height of the cylinder is 28 cm, and the radius is r cm, we have:
Surface area of the cylinder = 2πr * 28
The surface area of the cone can be calculated as follows:
Surface area of the cone = πr * l
Given that the slant height of the cone is 17 cm, we can find the slant height (l) using the Pythagorean theorem:
l^2 = r^2 + h^2
17^2 = r^2 + h^2
We also know that the total cost of coloring the solid is given as rs 2851.20, at a rate of rs 100 per sq cm. Hence, the total surface area (SA) can be calculated as:
SA = cost / rate
SA = 2851.20 / 100
The total surface area of the solid object is the sum of the surface area of the cylinder and the surface area of the cone:
Total surface area = Surface area of cylinder + Surface area of cone
Total surface area = 2πr * 28 + πr * l
Substituting the values, we get:
Total surface area = 2πr * 28 + πr * l
2851.20/100 = 2πr * 28 + πr * l
Now, we have two equations:
1) l^2 = r^2 + h^2
2) 2851.20/100 = 2πr * 28 + πr * l
Simplifying equation 1, we get:
289 - r^2 = h^2
Substituting this value into equation 2, we get:
2851.20/100 = 2πr * 28 + πr * l
2851.20 = 200πr + 100πl
Using the value of π as 22/7, we have:
2851.20 = 200 * (22/7) * r + 100 * (22/7) * l
2851.20 = 400 * (22/7) * r + 100 * (22/7) * l
2851.20 = (8800/7) * r + (2200/7) * l
Now, we have three equations:
1) l^2 = r^2 + h^2
2) 2851.20 = (8800/7) * r + (2200/7) * l
3) 289 - r^2 = h^2
From equation 1, we can solve for h^2:
h^2 = l^2 - r^2
Substituting this value into equation 3, we get:
289 - r^2 = l^2 - r^2
289 = l^2
Since both h^2 and l^2 are equal to 289, we have:
h^2 = l^2 = 289
Therefore, the height of the cone, h = sqrt(289) = 17 cm.