138k views
3 votes
A solid object formed with a combination of a cylinder and cone with same radius.The height of the cylinder and slant height of cone are 28 cm and 17cm.The total cost of colouring the solid at rate rs 100 per sq cm is rs 2851.20 find height of cone

1 Answer

5 votes

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.

User Xema
by
8.2k points