Mathematics
A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside.
If the height of the cone is 24 cm, the total height of the toy is 60 cm and the radius of the base of the cone = twice the radius of the base of the cylinder = 10 cm; find the total surface area of the toy. [Take π = 3.14]
Mensuration
ICSE
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Answer
Given,
Height of the cone (h) = 24 cm
Height of the cylinder (H) = 60 - 24 = 36 cm
Radius of the cone (r) = 10 cm
Given,
Radius of the base of the cone = Twice the radius of the base of the cylinder.
Radius of base of cylinder (R) = 5 cm.
By formula,
⇒ l2 = r2 + h2
⇒ l2 = 102 + 242
⇒ l2 = 100 + 576
⇒ l2 = 676
⇒ l = = 26 cm.
Total surface area of the toy = Surface area of the conical part + Base area of conical part + Surface area of the cylinder
= πrl + πr2 + 2πRH
= π(rl + r2 + 2RH)
= 3.14 × (10 × 26 + 102 + 2 × 5 × 36)
= 3.14 × (260 + 100 + 360)
= 3.14 × 720
= 2260.8 cm2.
Hence, total surface area of troy = 2260.8 cm2.
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