Answer:
Let's call the radius of the cylinder and cone "r".
The surface area of the cylinder is: 2πr(r + h) = 2πr^2 + 2πrh
The surface area of the cone is: πr(l + r) = πrl + πr^2
The total surface area of the solid object is the sum of the surface area of the cylinder and the cone: 2πr^2 + 2πrh + πrl + πr^2 = (2π + π)r^2 + 2πrh + πrl
We are given that the total cost of painting the solid object is Rs. 2851.20 and the rate of painting is Rs. 140 per 100 sq cm.
So the total surface area of the solid object is: 2851200/140 = 20580 sq cm
Now we can substitute the values we know into the equation for the total surface area: 20580 = (2π + π)r^2 + 2πrh + πrl
We also know that the height of the cylinder is 28 cm and the slant height of the cone is 17 cm.
We can use the Pythagorean theorem to find the height of the cone: h^2 + r^2 = (l/2)^2
Solving this equation for h, we get: h = √(l^2/4 - r^2)
Now we can substitute the given values and solve for the height of the cone:
h = √(17^2/4 - r^2) = √(289/4 - r^2)
We don't have any information about the radius of the cylinder and cone, so we cannot solve for h in terms of r, but we can find the height of the cone by assuming the value of radius.
Let's assume the radius of the cylinder and cone is 5cm.
h = √(289/4 - 5^2) = √(289/4 - 25) = √(289/4 - 25) = √(64) = 8cm
So, the height of the cone is 8cm.
Please note that this is a theoretical height as it is based on the assumption of radius being 5cm, the actual height of the cone may be different if the radius is different.