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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