Question

The radius and height of a right circular cone are in the ratio of 5:10 . if its 314 cubic cm , find its slant height.
( Take pie = 3.14 )​

Answer 1

Answer:

13cm

Step-by-step explanation:

v=1/3πr²h

k=1

l=√r²+h²

=√25+144

=13cm

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Answer 2

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The radius and height of a right circular cone are in the ratio of 5:10 . if its 314 cubic cm , find its slant height.

( Take pie = 3.14 )

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

${Slant \: height = \sqrt{r^{2} + \: h^{2} } }$

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Let height of the cone , h = 12x .

And radius of the cone , r = 5x.

Volume Of cone = 314 Cu.cm

$\small \: {Volume = 1 / 3\pi r^{2} h}$

$\therefore \small { \: \: 314 = \frac{1}{3} \times \frac{314}{100} \times 25x^{2 } \times 12x}$

$\rightarrow \: x^{3} = \frac{314 \times 3 \times 100}{314 \times 25 \times 12}$

$\rightarrow \: x^{3} = 1 \\ \rightarrow \: x = 1$

$\small{ \therefore \: Height \: of \: the \: cone \: , h \: = 12 × 1 \: = 12 cm \: }$

$\small \: {Hence \: , \: slant \: height = \sqrt{(12)^{2} + (5)^{2}} = \sqrt{144 + 25} = \sqrt{169} = 13 \: cm }$

Slant height = 13 cm .

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❒ More related formulas :-

Total Surface area of the cone = π r ( l + r)

Curved surface area of the cone = π r l

Circumference of the base = 2 π r

Volume of a cone is = 1 / 3 π r ^ 2 h

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