Mensuration-16

From Homeworkwiki

A right circular cylinder is mounted by a hemisphere such that the
top of the cylinder coincides with the lateral side of the hemisphere.
If the radius of the base of the cylinder is 3.5 cm and its
height is 10 cm, find its total volume.

Solution: Radius of the base of the cylinder, r = 3.5 cm and height h = 10 cm

Volume of the cylindrical part

= π r² h = 22/7 x 3.5² x 10 cu. cm

= 220/7 x 3.5 x 3.5 cu. cm

= 385 cu. cm

Volume of the hemispherical part

V = 2/3 x π r³ = 2/3 x 22/7 x 3.5³

= (44 x 3.5³) / (7 x 3) cu. cm

Taking log on both sides,

log V = log (44 x 3.5³) / (7 x 3)

= log 44 + 3 log 3.5 - log 21

= 1.6435 + 3 x 0.5441 - 1.3222

= 1.9536

Taking antilog on both sides,

V = antilog 1.9536 = 89.86 cu. cm

Total volume = 385 + 89.86 = 474.86 cu. cm