A toy in the shape of solid cylinder surmounted by a conical top If the height of the diameter of - Maths - Surface Areas and Volumes

Question

A toy in the shape of solid cylinder surmounted by a conical top
If the height of the diameter of the cylinder path are 21cm and
40cm respectively and height of the cone is 15cm Find the total
surface area of the toy use pie=3 14

Lalit Mehra · Accepted Answer

@niveditasister: Good answer! Keep posting!

Let r and h be the radius and height of the cylindrical part.

Suppose R and H be the radius and height of the conical top.

$Given, r = \frac{40}{2} cm = 20 cm and h = 21 cm$

R = 20 cm and H = 15 cm

Slant height of the cone, $l = \sqrt{R^{2} + H^{2}} = \sqrt{(20)^{2} + (15)^{2}} = \sqrt{625} = 25 cm$

Total surface of the toy

= Curved surface area of cone + Curved surface area of cylinder + Area of base

= πRl + 2πrh + πr²

= π(20 × 25 + 2 × 20 × 21 + 20 × 20) cm²

= 3.14 × (500 + 840 + 400) cm²

= 3.14 × 1740 cm²

= 5463.6 cm²

Thus, the total surface area of the toy is 5463.6 cm².

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A toy in the shape of solid cylinder surmounted by a conical top.If the height of the diameter of the cylinder path are 21cm and 40cm respectively and height of the cone is 15cm.Find the total surface area of the toy. use pie=3.14