AM-1677

Area between a curve and a line

A Math · Secondary 4 · Hard · Area between a curve and a line

A rectangle of width

x

cm and height

y

cm is inscribed in a semicircle of radius 10 cm with its base on the diameter. The top corners of the rectangle lie on the semicircle. Show that the area

A

of the rectangle is given by

A = x\sqrt{100 - x^2}

. What is

A

when

x = 6

$48\,\text{cm}^2$
$64\,\text{cm}^2$
$36\,\text{cm}^2$
$80\,\text{cm}^2$

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