Question

A right circular cylindrical container of base radius 6 cm and height 15 cm is full of ice
cream. The ice cream is to be filled in cones of height 9 cm and base radius 3cm, having a
hemispherical cap. Find the number of cones needed to empty the container.​

Answer 1

$\huge{ \underline{ \red{ \bold{ \underline{ \bf{Solution }}}}}}$

$\bf \red{Given} \purple{\begin{cases}\textsf{Radius\:of\:base=6cm}\\\textsf{height\:of\: cylinder=15cm}\\\textsf{height \:of \:cone=9cm}\\\textsf{Radius \:of\: base\: of\: cone=3cm } \end{cases}}$

$\large\underline{ \underline{ \pink{ \bold {To \:Find}}}}$

$\bf\red{we\:need \:to\:find \:the\:number\:of\:cones\:}$

$\bf\:141.43{cm}^{3}$

Thus the number of cones required

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \frac{1697.14 }{141.43}$

$\huge\bf\:{\boxed{\pink{=12}}}$

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Answer 2

$\bf\large{\underline{Question:-}}$

A right circular cylindrical container of base radius 6 cm and height 15 cm is full of ice

cream. The ice cream is to be filled in cones of height 9 cm and base radius 3cm, having a

hemispherical cap. Find the number of cones needed to empty the container.

$\bf\large{\underline{Solution:-}}$

• Voulme of ice-cream cone in container = πr²h

→ $\sf Volume\: of\: ice-cream\: cone\:in\: container=$

$\sf \frac{22}{7}×6^2×15$

→ $\sf 3.14 × 36 × 15$

→ $\sf 1697.14cm^3$

Now,

★ Volume of ice-cream = Volume of hemisphere + volume of cone

So,

→$\sf Volume\:of\:ice-cream = \frac{2}{3}πr^3 + \frac{1}{3}πr^2h$

→$\sf Volume\:of\:ice-cream = \frac{2}{3}\frac{22}{7}×3^3 + \frac{1}{3}\frac{22}{7}×3^2×9$

→$\sf Volume\:of\:ice-cream = 3^2×\frac{22}{7} [2+3]$

→$\sf Volume\:of\:ice-cream = 9×\frac{22}{7}×5$

→ $\sf Volume\:of\:ice-cream = 141.43cm^3$

$\bf{\underline{Hence:-}}$

• → Number of cone required = Volume of ice-cream in container ÷ volume of ice-cream .

• $\sf → No.\:of\:cone = \large\frac{1697.14}{141.43}$

• $\sf → No.\:of\: cones\: required= 12$

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