Question

A jewel box ( see fig.) is in the shape of a cuboid of dimensions 30 cm × 15 cm ×10 cm surmounted by a half part of a cylinder as shown in the figure. Then the volume of the box is​

Answer 1

Answer:

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Answer 2

i )Diameter of the semi-circle part = 7cm

∴ Radius, r = 3.5cm

∴ height of the box = 8 + radius ( r )

$:\implies\underline{\boxed{\sf{\red{Total~height=11.5~cm}}}}$

ii ) CSA of box = CSA of cuboidal part + CSA of semi-cylinder part.

$\sf{CSA ~of~ cuboidal~ part + 2 \times (20\times8)_{[front~side~wall]}+2(7\times8)_{[gide~wall]}+1(7\times20)_{[bottom]}}$

CSA of semi-cylinder part = area of semicircle + lateral surface area of toy cylinder.

$:\longmapsto \sf{\frac{1}{2}\pi r^2+\frac{1}{\not 2}\times \not 2\pi ~rl}\\\\:\longmapsto \sf{\frac{1}{2}\times\frac{22}{7}\times\frac{7}{2}\times\frac{7}{2}+\frac{22}{7}\times\frac{7}{2}\times20}\\\\:\longmapsto \sf{19.25+220}\\\\:\longmapsto \underline{\underline{\sf{239.25~cm^2}}}\\\\\therefore \sf\underline{Total~CSA~of~bor=572+239.265=211.25~cm^2}\\\\\underline{\boxed{\tt{\red{211.25~cm^2}}}}$

Ans. The volume of the box is 211.25 cm²​

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