A toy is in the shape of a solid cylinder surmounted by a conical top, if the height and diamater of the cylindrical part are 21 and 40 cm and the height of the cone is 15 cm then find the total surface area of the toy.
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Step-by-step explanation:
Radius= Diameter/2 =40/2
Radius=20cm
Height of cylinder=21cm
Height of cone=15cm
Slant height of cone,l=√ h2 + r2
l=√ (15)2 + (20)2
l=√ 225 + 400=√ 625
l=25cm
Total surface area of toy= Curved surface area of cone
+ Curved Surface area of cylinder+ Area of bottom part
Total surface area=πrl + 2πrhcyl + πr2
=3.14[20 × 25 + 2 × 20 × 21 + 20 × 20]
=3.14[1740]=5463.6cm2
TSA of the toy = CSA of Cylinder+ CSA of Cone+ area of bottom
= 2πrh+πrl+ πr2
= πr(2h+l+r)
= 22/7 × 20 ( 2 × 21 + 25+ 20 ) { l= 25 ( by using the formula : √h2+r2)}
= 440/7( 67)
= 62.85 × 87
= 5468.57 cm2
Hope it helps