Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th
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A right-angled triangle whose sides are 6 cm, 8 cm and 10 cm is revolved about the sides containing the right angle in two ways. Find the difference in volumes of the two solids so formed. - Mathematics

Sum

A right-angled triangle whose sides are 6 cm, 8 cm and 10 cm is revolved about the sides containing the right angle in two ways. Find the difference in volumes of the two solids so formed.

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Solution

Three sides of a triangle are 6 cm, 8 cm and 10 cm.

Case (i): If the triangle is revolved about the side 6 cm, the cone will be formed with radius 6 cm and height 8 cm.

Volume of the cone = `1/3 pi"r"^2"h"` cu. units

= `1/3 xx pi xx 6 xx 6 xx 8`

=  96π cm

Case (ii): If the triangle is revolved about the side 8 cm, the cone will be formed with radius 8 cm and height 6 cm.

Volume of the cone = `1/3 xx pi xx 8 xx 8 xx 6`

= 128π cm 

Difference in volume of the two solids

= (128π – 96π) cm3 

= 32π cm3 

= `32 xx 22/7` cm

= 100.57 cm

The difference in the volume of the two solids = 100.57 cm3

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

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 7 Mensuration
Exercise 7.2 | Q 5 | Page 290
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