Question

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. The heap is to
be covered by canvas to protect it from rain. If you want to fill this wheat into boxes of dimensions
3.5 m long, 2.5 m wide and 1 m deep, how many such boxes are required?
Find the
i) volume of the heap ii) area of canvas

Answer 1

$\blue{\frak{Given}}\begin{cases}& \sf{Diameter\:= \frak{10.5}}\\ & \sf{Radius\:(r)\:=\:{\frac{10.5}{2}}\:cm\:= \frak{5.25\:m}}\\ & \sf{Height\:= \frak{3\:m}}\end{cases}$

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Need to find : Volume of the Heap & Area of Canvas.

$\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━$

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$\:\:\:\:\:\:\:\:\:\:\:{\bold{\dag}}\:{\sf{As\:we\:know\:that\::}}$

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$\:\:\:\:\:\:\:\:{\red{\bigstar}}\:\sf{Volume\:=\:{\dfrac{1}{3}}{\pi r}^{2}h}$

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:{\sf{\dfrac{1}{3}}\:\times\:{\dfrac{22}{7}}\:\times\:(5.25)^{2}\:\times\:3}$

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:{\sf{\bold{86.625\:m}^{\bold{3}}}}$

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• ${\underline{\underline{\sf{\bf{\pink{Slant\:Height\::\sqrt{r²\:+\:h²}}}}}}}$

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:{\sf{\sqrt{(5.25)²\:+\:(3)²}}}$

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:{\sf{\sqrt{27.5625\:+\:9}}}$

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:{\sf{\sqrt{36.5625}}}$

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:{\sf{6.05\:m}}$

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:{\sf{6.05\:m\:{\bold{[approx.]}}}}$

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$\:\:\:\:\:\:\:\:\:\:\:{\bold{\dag}}\:{\sf{As\:we\:know\:that\::}}$

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$\:\:\:\:\:\:\:\:{\red{\bigstar}}\:\sf{Curved\:Surface\:Area\:=\:\pi rl}$

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:{\sf{\dfrac{22}{7}}\:\times\:5.25\:\times\:6.05}$

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$\:\:\:\:\:\:\:\::\:\Longrightarrow\:{\sf{99.825\:m²}}$

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$\:\therefore\:{\underline{\sf{Hence,\:the\:Area\:of\:the\:Canvas\:required\:is\:{\textsf{\textbf{99.825\:m²}}}}}}.$

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$\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━$

${\purple{\sf{\bf{@ℐᴛᴢӇᴀᴘᴘʏҨᴜᴇᴇɴ࿐}}}}$

Answer 2

Step-by-step explanation:

Csa = πrl = 3.14 × 5.25 × 6.05

Area of the Canvas required is 99.825m²