Question

A certain number of bacteria was cultivated. The number of bacteria increased by 10%in first hour, then decreased by 10% in the second hour and again increased by 10% in the third hour. Find the original number of bacteria, if the final count is 10,890

Please Give Honest Answer
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Answer 1

Given:

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Curved surface area of cone = 60π cm²

Slant height of cone = 8 cm

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To find:

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Diameter of base of cone?

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Solution:

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☯ Let radius of cone be r cm.

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$\setlength{\unitlength}{1.5mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf{r}}\put(22,10){\sf{8 cm}}\end{picture}$

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We know that,

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$\star\;{\boxed{\sf{\purple{CSA_{\;(cone)} = \pi rl}}}}$

$:\implies\sf \cancel{\pi} \times r \times 8 = 60 \cancel{\pi}$

$:\implies\sf r \times 8 = 60$

$:\implies\sf r = \cancel{ \dfrac{60}{8}}$

$:\implies{\boxed{\sf{\pink{r = 7.5\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Thus,\;Radius\;of\;cone\;is\; \bf{7.5\;cm}.}}}$

We know that,

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Diameter = 2 × Radius

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Therefore,

Diameter of base of cone is 15 cm.

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$\qquad\qquad\boxed{\underline{\underline{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}$

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$\sf (i)\;Total\;surface\;area\;of\;cone\; = \; \red{\pi r(r + l)}$

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$\sf (ii)\;Volume\;of\;cone\; = \; \purple{ \dfrac{1}{3} \pi r^2 h}$