Question

a wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder if the height of the cylinder is 10cm and is base is of radius 3.5cm find the volume of wood in the toy

Answer 1

answer : 616/3 cm³

explanation : volume of wood in the toy = volume of cylindrical wood - 2 × volume of hemispherical wood

[ actually, a toy was made by scooping out a hemisphere of same radius from each end of solid cylinder]

volume of cylinderical wood = πr²l

= 22/7 × (3.5cm)² × 10cm

= 22/7 × 7/2 × 7/2 × 10

= 11× 7 × 5

= 385 cm³

volume of hemispherical wood = 2/3πr³

= 2/3 × 22/7 × (3.5cm)³

= 2/3 × 22/7 × 7/2 × 7/2 × 7/2

= 11 × 7 × 7/6

= 539/6 cm³

so, volume of wood in the toy = 385cm³ - 2× 539/6 cm³

= (385 × 3 - 539)/3 cm³

= 616/3 cm³

Answer 2

Answer:

Volume of the wooden toy =

$\frac{616}{3}\: square \: cm$

Step-by-step explanation:

Radius of cylinder = Radius of Hemisphere = r = 3.5cm

Height of the cylinder (h)=10cm

Volume of the toy

=$volume \: of \: the \:cylinder \\- 2\times volume \:of \:hemisphere$

=$\pi r^{2}h - 2\times \frac{2}{3} \pi r^{3}$

=$\pi r^{2} \times \left(h-\frac{4}{3}\times r \right)$

= $\frac{22}{7} \times 3.5^{2} \times \left(10-\frac{4}{3} \times 3.5 \right)$

= $\frac{22}{7} \times 12.25 \times \left(\frac{(30-14)}{3}\right)$

=$22 \times 1.75 \times \frac{16}{3}$

= $\frac{616}{3}\: square \: cm$

Therefore,.

Volume of the wooden toy =

$\frac{616}{3}\: square \: cm$

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