Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# 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.

#### 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

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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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