Q3 of 24 Page 227

Amina has drawn a right-angled triangle whose lengths of two sides adjacent to right angle are 15cm and 20 cm. Let us determine the curved surface area, total surface area and volume of the solid which is formed by taking the side of length 15cm. which is formed by completely revolving the triangle once around the side of the triangle with the length of 15cm, having been taken as an axis.

1.JPG


2.JPG


The solid formed by taking the side of length 15 cm and completely revolving the triangle once is a right circular cone.


According to problem,


Height of the cone, h = 15 cm


Length of base radius, r = 20 cm


∴ slant height, l = √(h2 + r2)√(152 + 202) = √(225 + 400) = 25 cm


∴ curved surface area,


= πrl


= 22/7 × 20 × 25


= 1571.43 sq. cm.


∴ Total surface area,


= πr2 + πrl


= 22/7 × 202 + 1571.43


= 1257.14 + 1571.43


= 2828.57 sq cm.


∴ volume,


= πr2h/3


= 22/7 × 202 × 15/3


= 6285.71 cubic cm.


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 4

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