SOLUTION: The curve surface area of a cylinder is 1.5 times the total surface area of a cone. If the diameter of the cylinder and cone are equal to 10cm and the vertical height of the cone i

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Question 1210537: The curve surface area of a cylinder is 1.5 times the total surface area of a cone. If the diameter of the cylinder and cone are equal to 10cm and the vertical height of the cone is 12cm. Calculate the height of the cylinder
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(2189)   (Show Source): You can put this solution on YOUR website!
To find the height of the cylinder, we first need to determine the total surface area of the cone and then use the relationship provided to solve for the cylinder's height.
### 1. Find the Dimensions of the Cone
We are given the diameter of the cone is **10 cm**, so the radius () is **5 cm**. The vertical height () is **12 cm**.
To find the Total Surface Area (TSA) of a cone, we first need the **slant height ()**:

### 2. Calculate the Total Surface Area (TSA) of the Cone
The formula for the TSA of a cone is :

---
### 3. Calculate the Curved Surface Area (CSA) of the Cylinder
The problem states that the CSA of the cylinder is **1.5 times** the TSA of the cone:

### 4. Solve for the Height of the Cylinder ()
The formula for the Curved Surface Area of a cylinder is . We know the diameter is 10 cm, so the radius () is **5 cm**:

Now, divide both sides by :

**The height of the cylinder is 13.5 cm.**
Would you like me to calculate the volume of either shape to see how they compare?
Answer by ikleyn(53575)   (Show Source): You can put this solution on YOUR website!
.
The curve surface area of a cylinder is 1.5 times the total surface area of a cone.
If the diameter of the cylinder and cone are equal to 10cm and the vertical height of the cone is 12cm.
Calculate the height of the cylinder
~~~~~~~~~~~~~~~~~~~~~~~~~ 

The curve surface area of this cylinder is  

     =  =  = .


The slant height of the cone is  

    L =  =  =  = 13 cm.


The total surface area of the cone is 

     =  +  =  +  =  = .


Now write the equation   = 

     = 


Simplify it

     h = 1.5*9 =  13.5.


ANSWER.  The height of the cone is 13.5 cm.

Solved.



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