Question

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is 12 cm and its base is of radius 4.2 cm, find the total surface area of the article. Also, find the volume of the wood left in the article.
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Answer 1

➝ Given :-

→ Radius of the hemsphere,r = 4.2cm

→ Radius of the hemsphere,r = 4.2cm

→ Radius of the cylinder, r = 4.2cm

➝ To find :-

→ volume of the wood left in the article

➝ Solution :-

→ total surface area of the article = curved surface area of cylinder + curved surface area of 2 hemisphere

$= 2\pi rh \: + 2 \times 2\pi {r}^{2} \\ = 2\pi \:rh + 4\pi {r}^{2} \\ = 2\pi r(h + 2r) \\ = [2 \times \frac{22}{7} \times 4.2 \times (12 + 2 \times 4.2)] {cm}^{2} \\ = (26.4 \times 20.4) {cm}^{2} \\ = 538.56 {cm}^{2}$

→ Total volume of the wood left in the article

= vol of the cylinder - vol of 2 hemisphere

$= \pi {r}^{2} h \: - \: 2 \times \frac{2}{3} \pi {r}^{3} \\ = \pi {r}^{2} (h \: - \: \frac{4}{3} r) \\ = [\frac{22}{7} \times 4.2 \times 4.2 \times (12 - \frac{4}{3} \times 4.2)] {cm}^{3} \\ = (55.44 \times 6.4) {cm}^{3} \\ = 354.815 {cm}^{3}$

hence, the volume of the wood left in the article is 354.815 cm³

Answer 2

Data:-

R of hemisphere=4.2

R of cylinder=4.2

V of wooden left in article=?

SOL:

TSA of article=CSA of cylinder +CSA of 2

hemisphere

=2πrh+22×2πr^

=2πrh+4πr^

=2πr(h+2r)

=[2×22/7×4.2×(12+2×4.2)]cm^

=(26.4×20.4)cm^

=538.56cm2^

Total volume of wooden left in article

= volume of the cylinder- volume of 2 hemisphere

=πr^h−2×2/3πr3

=πr2(h−4/3r)

=[22/7×4.2×4.2×(12−4/3×4.2)]cm3

=(55.44×6.4)cm3

=354.815cm3