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Cylinder, Cone and Sphere — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsCylinder, Cone and Sphere5 Marks
Question
Two solid cylinders, one with diameter $60 \ cm$ and height $30 \ cm$ and the other with radius $30 \ cm$ and height $60 \ cm,$ aremetledandrecastedinto a third solid cylinder of height $10 \ cm.$ Find the diameter of the cylinder formed.
✓

Answer

For cylinder $1,$
Height $= h_1 = 30 \ cm$
Radius $=r_1=\frac{60}{2}=30 \ cm$
Volume $= V _1=\pi r _1^2 h _1=\pi \times 30 \times 30 \times 30=27000 \pi \ cm ^3$
For cylinder $2 ,$
Height $= h_2 = 60 \ cm$
Radius $= r_2 = 30 \ cm$
Volume $= V _2=\pi r _2^2 h _2=\pi \times 30 \times 30 \times 60=54000 \pi \ cm ^3$
Let r be the radius of the third cylinder.
Height $= h = 10 \ cm$
Volume $= V = \pi r^2h = \pi r^2 \times 10$
Now,
$V = V_1 + V_2$
$\Rightarrow \pi r^2 \times 10 = 27000 \pi + 54000 \pi$
$\Rightarrow \pi r^2 \times 10 = 81000 \pi$
$\Rightarrow r^2 = 8100$
$\Rightarrow r = 90$
$\Rightarrow$ Diameter $= 2r = 180 \ cm$

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