A rocket is in the form of a circular cylinder closed at the lower end and a cone of the same radius is attached to the top. the radius of the cylinder is 2.5 m, its height is 21 m and the slant height of the cone is 8 m. calculate the total surface area of the rocket.
Answers
There is a mistake in this question. The slant height of the cone should be 8 m instead of 8 cm.
Curved surface area of cone = πrl
= 22/7*2.5*8
= 440/7
= 62.86 sq m
Curved surface area of cylinder = 2πrh
= 2*22/7*2.5*21
= 330 sq m
Area of the base circle of the cylinder = πr²
= 22/7*2.5*2.5
= 19.64 sq m
Total surface area of rocket = 62.85 + 330 + 19.64
= 412.5 sq m
Volume of cylinder = πr²h
= 22/7*2.5*2.5*21
= 412.5 cu m
Now
h² = 8² - (2.5)²
h² = 64 - 6.25
h² = 57.75
h = √57.75
h = 7.6 m
Volume of the cone = 1/3πr²h
= 1/3*22/7*2.5*2.5*7.6
= 49.76 cu m
Total volume of rocket = 412.5 + 49.76
= 462.26 cu m
Answer:
Total surface area of rocket is 412.5 m² and the Volume of the rocket is 462.26 m³.
Step-by-step explanation:
Given :
Radius of the cylinder and cone , r = 2.5 m
Height of a cylinder, h = 21 m
Slant height of the cone , l = 8 m
Curved surface area of cone = πrl
= 22/7 × 2.5 × 8
= 440/7
CSA of cone = 62.86 m²
Curved surface area of cylinder = 2πrh
= 2 × 22/7 × 2.5 × 21
CSA of cylinder = 330 m²
Area of the base of the cylinder = πr²
= 22/7 × 2.5 × 2.5
= 19.64 m²
Total surface area of rocket = CSA of cone + CSA of cylinder + Area of the base of the cylinder
TSA of rocket = 62.85 + 330 + 19.64 = 412.5 m²
Total surface area of rocket = 412.5 m²
Volume of cylinder = πr²h
= 22/7 × 2.5 × 2.5 × 21 = 22 × 2.5 × 2.5 × 3
Volume of cylinder = 412.5 m³
Height of the cone, h1 = √l² - r²
h1 = √8² - (2.5)²
h1 = √64 - 6.25
h1 = √57.75
h1 = 7.59 m
Volume of the cone = 1/3πr²h1
= ⅓ × 22/7× 2.5 × 2.5 × 7.59
= 49.76 m³
Volume of the rocket = 412.5 + 49.76 = 462.26 m³
Hence, Total surface area of rocket is 412.5 m² and the Volume of the rocket is 462.26 m³.
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