The sides containing right angles of a right angled triangle are 8 cm and 6 cm it is rotated about its hypotenuse . Find the volume and total surface area of the solid formed.
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Given:
The sides of a right angled triangle are 8 cm and 6 cm.
To find:
the volume and total surface area of the solid formed.
Solution:
1) In the given triangle the hypotenuse of the triangle must be 10 cm by the Pythagoras theorem.
2) If the given triangle is rotated by the hypotenuse then the resultant figure we get as the two cone whose common chord must given by 8×6/10 = 4.8 cm.
3) Volume of the figure given by the addition of the volume of the two cones
v = πr²h
= 22/7×4.8×4.8×10
= 723.456 cm³
4) The total surface area of the solid is given by the CSA of the two solid cones:
A = πr(L₁+L₂)
= 22/7×4.8(8+6)
= 21.94 cm²
The volume and total surface area of the solid formed 723.456 cm³ and 21.94 cm².
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