Question

A heap ofrice is in the form of cone of base diameter 30 m and height 3.5m. How much canvas cloth is required to just cover the heap? (plz do solutions plz)​

Answer 1

Given that: A heap of rice is in the form of cone. Diameter of the base is 30m and it's height is 3.5m.

Need to Find: The Canvas cloth required to just cover the heap

Formula Used:

$\leadsto\tt{ l =\sqrt{{h}^{2}+{r}^{2}}}$$\\ \leadsto\tt{Curved\: surface\: area\: of\: cone=\pi\times r\times l}$

• l is slant height of the cone
• h is height of the cone
• r is Radius of the cone

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Solution:

It is given that::

$\mapsto\sf{Diameter=d=30\: m}$

$\therefore\sf{Radius=r=\dfrac{d}{2}=\dfrac{30}{2}=15\: m}$

$\mapsto\sf{Height=h=3.5\: m}$

We have to find the Canvas cloth required to just cover the heap, that is we have to find the Curved surface area of cone. For finding the Curved surface area of cone we firstly need it's Slant height. So, Let's firstly find the Slant height of cone.

$\\ \: \: \: \: \: \: \: \longrightarrow \sf{l=\sqrt{{h}^{2}+{r}^{2}}}$

$\\ \: \: \: \: \: \: \: \longrightarrow \sf{l=\sqrt{{3.5}^{2}+{15}^{2}}}$

$\\ \: \: \: \: \: \: \: \longrightarrow \sf{l=\sqrt{12.25+225}}$

$\\ \: \: \: \: \: \: \: \longrightarrow \sf{l=\sqrt{237.25}}$

$\\ \: \: \: \: \: \: \: \longrightarrow \bold{l=\color{red}{15.40\: m}}$

• Henceforth, Slant height of cone is 15.40m

Now,

$\\ \: \: \: \: \: \: \: \implies \sf{Curved\: surface\: area\: of\: cone=\pi\times r\times l}$

$\\ \: \: \: \: \: \: \: \implies \sf{Curved\: surface\: area\: of\: cone=\frac{22}{7}\times 15\times 15.40}$

$\\ \: \: \: \: \: \: \: \implies \sf{Curved\: surface\: area\: of\: cone=\frac{22}{7}\times 231}$

$\\ \: \: \: \: \: \: \: \implies \bold{Curved\: surface\: area\: of\: cone=\color{red}{726\: {m}^{2}}}$

Required Answer:

Hence, the canva cloth required to just the cover the heap is $\color{purple}\bold{726\: {m}^{2}}$

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More to Know: $\\\dashrightarrow\sf{Total\: Surface\: area\: of\: Cone=(\pi {r}^{2}+\pi r l)}$

$\dashrightarrow\sf{Volume\: of\: cone=\dfrac{1}{3}\pi {r}^{2}h}$

• r is Radius of Cone
• l is Slant height of Cone
• h is Height of Cone