Question

A metal cuboid of dimension 22 cm ×15 cm×7.5cm was melted and cast into a cylinder of height 14 cm what is its radius

Answer 1

$\huge\underline\blue{\sf Answer:}$

$\red{\boxed{\sf Radius\:of\: Cylinder (r)=7.5cm }}$

$\huge\underline\blue{\sf Solution:}$

$\large\underline\pink{\sf Given: }$

• Lenght of cuboid (l) = 22cm

• Breadth of cuboid (b) = 15cm

• Height of cuboid (h) = 7.5cm

• Height of cylinder (H) = 14cm

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

• Radius of cylinder (r) = ?

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$\large\underline{\underline{\sf According\:to\: Question:}}$

${\boxed{\sf Volume\:of\: cylinder=Volume\:of\:metal\:cuboid }}$

$\large\implies{\sf πr^2H=l×b×h }$

$\large\implies{\sf \frac{22}{7}×r^2×14=22×15×7.5 }$

$\large\implies{\sf 22×r^2×2=22×15×7.5}$

$\large\implies{\sf r^2=\frac{22×15×7.5}{22×2} }$

$\large\implies{\sf r^2=\frac{112.5}{2} }$

$\large\implies{\sf r^2=56.25}$

$\large\implies{\sf r=\sqrt{56.25}}$

$\large\implies{\sf r=7.5\:cm}$

$\red{\boxed{\sf Radius\:of\: Cylinder (r)=7.5cm }}$