# A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the slant height of the conical portion is 5 cm, find the total surface area and volume of the rocket [Use π = 3.14]

**Solution:**

Given, a rocket in the form of a right circular cylinder closed at the lower end is surmounted by a cone with the same radius as that of the cylinder.

The diameter and height of the cylinder are 6 cm and 12 cm.

We have to find the surface area and volume of the rocket if the slant height of the conical portion is 5 cm.

Volume of the rocket = volume of cylinder + volume of cone

Volume of cylinder = πr²h

Given, diameter = 6 cm

Radius = 6/2 = 3 cm

h = 12 cm

Volume = (3.14)(3)²(12)

= (3.14)(9)(12)

= 339.12 cm³

Volume of cone = (1/3)πr²h

Given, l = 5 cm

r = 3 cm

We know, l² = r² + h²

(5)² = (3)² + h²

25 = 9 + h²

h² = 25 - 9

h² = 16

Taking square root,

h = 4 cm

So, volume of cone = (3.14)(1/3)(3)²(4)

= (3.14)(3)(4)

= 12(3.14)

= 37.68 cm³

Volume of rocket = 339.12 + 37.68

= 376.8 cm³

Therefore, the volume of the rocket is 376.8 cm³

Total surface area of rocket = curved surface area of cylinder + curved surface area of cone + area of base

Curved surface area of cylinder = 2πrh

= 2(3.14)(3)(12)

= 226.08 cm²

Curved surface of cone = πrl

= 3.14(3)(5)

= 47.1 cm²

Area of base = πr²

= (3.14)(3)²

= 3.14(9)

= 28.26 cm²

Total surface area of rocket = 226.08 + 47.1 + 28.26

= 301.44 cm²

Therefore, the total surface area of the rocket is 301.44 cm².

**✦ Try This: **A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 8 cm and 16 cm, respectively. If the slant height of the conical portion is 4 cm, find the total surface area and volume of the rocket [Use π = 3.14].

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 13

**NCERT Exemplar Class 10 Maths Exercise 12.4 Problem 14**

## A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the slant height of the conical portion is 5 cm, find the total surface area and volume of the rocket [Use π = 3.14]

**Summary:**

A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the slant height of the conical portion is 5 cm, the total surface area and volume of the rocket are 376.8 cm³ and 301.44 cm²

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