A toy is in the shape of a solid cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 21 cm and 40 cm respectively, and the height of cone is 15 cm, then find the total surface area of the toy. [π = 3.14, be taken]
★ REQUIRED FULL EXPLANATION ANSWER
Answers
★ Question :
A toy is in the shape of a solid cylinder surmounted by a conical top . If the height and diameter of the cylindrical part are 21 cm and 40 cm respectively, and the height of cone is 15 cm, then find the total surface area of the toy .
[ π = 3.14, be taken ]
★ Solution :
[ Read the question twice ]
Total Surface Area = TSA
Curved Surface Area = CSA
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⧪ For Cylindrical part :
Height (h) = 21 cm
Diameter (d) = 40 cm
⇒ Radius (r) = 20 cm
CSA of Cylinder = 2πrh
⧪ For Conical part :
Height (h) = 15 cm
Radius of cone = Radius of cylinder ( Since both bases are joined )
Radius (r) = 20 cm
Apply Pythagoras theorem to find slant height (l) ,
➠ l² = r² + h²
➠ l² = (20)² + (15)²
➠ l² = 400 + 225
➠ l² = 625
➠ l² = (25)²
➠ l = 25 cm
Slant height (l) = 25 cm
CSA of cone = πrl
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TSA of Toy = CSA of Cylinder + CSA of Cone + Area of base of cylinder
➠ TSA of Toy = 2πrh + πrl + πr²
CSA of Cylinder = 2πrh
➠ CSA of Cylinder = 2(3.14)(20)(21)
➠ CSA of Cylinder = 2637.6 cm²
CSA of Cone = πrl
➠ CSA of Cone = (3.14)(20)(25
➠ CSA of Cone = 1570 cm²
Area of base of cylinder = πr²
➠ Area of base of cylinder = (3.14)(20)²
➠ Area of base of cylinder = 1256 cm²
TSA of Toy = CSA of Cylinder + CSA of Cone + Area of base of cylinder
➠ TSA of Toy = 2637.6 + 1570 + 1256
➠ TSA of Toy = 5463.6 cm²
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Answer:
770cm²
Step-by-step explanation:
Height of the cylindrical part =13cm
Radius of cone , cylinder and hemi sphere=5cm
r=5cm for hemisphere cylinder and cone.
Height of cone h=30−5−13=12
The area of canvas required=Surface area of hemishphere,cylinder and cone parts of tent
A=2πr2+2πrH+πr(h2+r2)
A=2π×5×5+2π×5×13+π×5(52+122)
A=770cm²