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  • A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume and the curved surface of the solid so formed.

A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume and the curved surface of the solid so formed.

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Answer : Volume =301.44\; cm^{3} and Curved surface area =188.57\; cm^{2}

A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm.

So on revolving we get a right circular cone as shown in the figure.

Radius = 6 cm, Height = 8 cm, Slant Height = 10 cm

Now, we know that Volume of cone=\frac{1}{3}\pi r^{2}h                    (where r is radius and h is height)

V=\frac{1}{3}\times 3.14 \times \left ( 6 \right )^{2}\times 8

      =\frac{1}{3}\times 3.14 \times 36 \times 8

      =\frac{1}{3}\times 12 \times 8

     =301.44\; cm^{3}

Curved surface area =\pi r l                        (where r is radius and l is slant height)

=\frac{22}{7}\times 6\times 10

=\frac{1320}{7}

=188.57\; cm^{2}

Hence Volume =301.44\; cm^{3} and curved surface area =188.57\; cm^{2}

 

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