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A right triangle whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate.) - Mathematics

A right triangle whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate.)

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Solution

The double cone so formed by revolving this right-angled triangle ABC about its hypotenuse is shown in the figure.

Hypotenuse AC = `sqrt(3^2+4^2)`

=`sqrt25` = 5 cm

Area of ΔABC = 1/2 x AB x AC

`1/2xx AC xx OB = 1/2xx4xx3`

`1/2xx5xxOB = 6`

OB = 12/5 = 2.4 cm

Volume of double cone = Volume of cone 1 + Volume of cone 2

`=1/3 pir^2h_1 + 1/3 pir^2h_2`

`=1/3pir^2(h_1+h_2)=1/3pir^2(OA+OC)`

`=1/3xx3.14xx(2.4)^2(5)`

=30.14 cm3

Surface area of double cone = Surface area of cone 1 + Surface area of cone 2

= πrl1 + πrl2

= πr[4+3] = 3.14 x 2.4 x 7

= 52.75 cm2

  Is there an error in this question or solution?
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APPEARS IN

NCERT Class 10 Maths
Chapter 13 Surface Areas and Volumes
Exercise 13.4 | Q 2 | Page 258
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