Question

A wooden article was made by scooping out a hemisphere on each end of a solid cylinder.If the height of the cylinder is 10m and the radius of the base is 3.5m, find the tsa of the article

Answer 1

A wooden article is scooped out a hemisphere from both sides therefore,
Radius of hemispheres = Radius of cylinder = 3.5m
Height of the cylinder = 10m
Now as the bases of cylinder are occupied by the two hemispheres therefore ewe will take the Curved surface area of cylinder and hemispheres.
T.S.A of the article = C.S.A of cylinder+ C.S.A of upper hemisphere +C.S.A of lower hemisphere
$= 2\pi rh + 2\pi {r}^{2}+ 2\pi {r}^{2} \: \\ = 2\pi r(h + r + r ) \\ = 2 \times\binom{22}{7} \times 3.5 \times (10 + 3.5 + 3.5) \\ = 44 \times 0.5 \times (17) \\ = 22 \times 17 \\ = 374 {cm}^{2}$
Therefore the T.S.A of the article is 374cm^2