Shanta runs an industry in a shed which is in | vedclass

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(B) The volume of air inside the shed (when there are no people or machinery) is given by the sum of the volume of the cuboid and the volume of the ha

Vedclass · Accepted Answer

$827.15$

Vedclass · Answer

(B) The volume of air inside the shed (when there are no people or machinery) is given by the sum of the volume of the cuboid and the volume of the half cylinder.The dimensions of the cuboid are $length = 15\,m,$ $breadth = 7\,m,$ and $height = 8\,m.$Volume of cuboid $= length 	imes breadth 	imes height = 15 	imes 7 	imes 8 = 840\,m^3.$The half cylinder has a diameter of $7\,m,$ so its radius $r = 3.5\,m = \frac{7}{2}\,m.$ The length of the cylinder is $15\,m.$Volume of half cylinder $= \frac{1}{2} 	imes (\pi r^2 h) = \frac{1}{2} 	imes \frac{22}{7} 	imes \frac{7}{2} 	imes \frac{7}{2} 	imes 15 = 288.75\,m^3.$Total volume of the shed $= 840 + 288.75 = 1128.75\,m^3.$Space occupied by machinery $= 300\,m^3.$Space occupied by $20$ workers $= 20 	imes 0.08 = 1.6\,m^3.$Total space occupied $= 300 + 1.6 = 301.6\,m^3.$Volume of air in the shed $= 1128.75 - 301.6 = 827.15\,m^3.$

Part $I$	Part $II$
$1.$ Volume of a cuboid	$a.$ $\frac{1}{3} \pi r^{2} h$
$2.$ Volume of a cone	$b.$ $\pi r^{2} h$
$3.$ Volume of a cylinder	$c.$ $\frac{4}{3} \pi r^{3}$
$4.$ Volume of a sphere	$d.$ $lbh$

Similar Questions

The base of a cone with radius $6 \, cm$ and height $8 \, cm$ is hemispherical. Find the curved surface area and the volume of the solid. $(\pi = 3.14)$

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Which of the following correctly matches the information given in Part $I$ and Part $II$?

Part $I$ Part $II$

$1.$ Volume of a cuboid $a.$ $\frac{1}{3} \pi r^{2} h$

$2.$ Volume of a cone $b.$ $\pi r^{2} h$

$3.$ Volume of a cylinder $c.$ $\frac{4}{3} \pi r^{3}$

$4.$ Volume of a sphere $d.$ $lbh$

$1 \text{ litre} = \dots \text{ cm}^3$

The base of a cone is hemispherical. The radius of the cone is $15 \, cm$ and the total height of the solid is $55 \, cm$. Find the volume of this solid (in $cm^3$).

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