A rocket is in the form of a circular cylinder closed at the lower end with a cone of the same radius attached to the top. The cylinder is of radius and height and the cone has the slant height . Calculate the total surface area and the volume of the rocket.

According to the question it is given that,

Radius of the cylindrical portion of the rocket (R)

Height of the cylindrical portion of the rocket (H)

Slant Height of the Conical surface of the rocket (L)

Curved Surface Area of the Cone

Then,

Curved Surface Area of the Cone

Thus, the total curved surface area S is

Now, the total Surface Area of the Conical Surface

Then, calculating the volume of the rocket

Volume of the conical part of the rocket

Assume, h be the height of the conical portion in the rocket.

We all know that,

Using the value of h, we will get

Volume of the conical part

Then,

Volume of the Cylindrical Portion

Thus, the total volume of the rocket

Hence, the total volume of the Rocket is