A rocket is in the form of a circular cylinder closed at the lower end with the cone of the same base radius attach to the top the cylinder is of radius 2 5 m and height 21 m & the cone has slant height 8cm find the total surfce area of the volume of the rocket .
Answers
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.
HOPE THIS ANSWER WILL HELP YOU….
Given radius of the cylindrical portion of the rocket (say, R) = 2.5m
Given height of the cylindrical portion of the rocket (say, H) = 21m
Given Slant Height of the Conical surface of the rocket (say, L) = 8m
Curved Surface Area of the Cone (say S1) = RL
S1 = m2 ……. E.1
Curved Surface Area of the Cone (say, S2) = 2RH + R2
S2 = (2 π 2.5 21) + (π (2.5)2 )
S2 = (π 105) + (π 6.25) …….. E.2
So, The total curved surface area = E.1 + E.2
S = S1 + S2
S = (π 20) + (π 105) + (π 6.25)
S = 62.83 + 329.86 + 19.63
S = 412.3 m2
Hence, the total Curved Surface Area of the Conical Surface = 412.3 m2
Volume of the conical surface of the rocket = 13×227×R2×h
V1 = 13×227×(2.5)2×h ……. E.3
Let, h be the height of the conical portion in the rocket.
Now,
L2 = R2 + h2
h2 = L2 – R2
h = L2−R2−−−−−−−√
h = 82−2.52−−−−−−−√
h = 23.685 m
Putting the value of h in E.3, we will get
Volume of the conical portion (V1) = 13×227×2.52×23.685 m2 …….. E.4
Volume of the Cylindrical Portion (V2) = πR2h
V2 = 227×2.52×21
So, the total volume of the rocket = V1 + V2
V = 461.84 m2
Hence, the total volume of the Rocket (V) is 461.84 m2