Question

from the rectangular metal sheet of side 30 cm and 40 centimetre a circular sheet as big as possible is cut off find the area of remaining sheet ​

Answer 1

Answer:

Step-by-step explanation:

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Diameter of circular sheet = 30 cm , So radius of circular sheet = 15 cm

Area of remaining sheet = Area of rectangular sheet - Circular sheet

Area of remaining sheet = Length × Breadth - π r2

Area of remaining sheet = 40 × 30 - 227× 15× 15

Area of remaining sheet = 1200 - 49507

Area of remaining sheet = 1200 - 707.14

Area of remaining sheet = 492.86 cm2 ( Ans )

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Answer 2

The diameter of the greatest possible circular sheet which can be carved out from the rectangular sheet, should be equal to the shortest side, i.e., the breadth of the rectangular sheet, 30 cm.

$\quad$

$\therefore\ 2r=30\ cm$

$\quad$

Then the area of the remaining portion will be,

$\quad$

$A=l(2r)-\pi r^2\\\\\\A=2lr-\dfrac {\pi (2r)^2}{4}\\\\\\A=2r\left(l-\dfrac {\pi(2r)}{4}\right)\\\\\\A=30\left(40-\dfrac {30\pi}{4}\right)\\\\\\\underline {\underline {A\approx493.14\ cm^2}}$