Find the perimeter and area of the shaded por | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Area of the shaded portion = (Area of the rectangle) - (Area of the four sectors).Each sector is a quadrant of a circle with radius $r = 10\, cm$.

Vedclass · Accepted Answer

$90.8\, cm, 414\, cm^2$

Vedclass · Answer

(A) Area of the shaded portion = (Area of the rectangle) - (Area of the four sectors).Each sector is a quadrant of a circle with radius $r = 10\, cm$. The four quadrants together form a full circle of radius $10\, cm$.Area of the rectangle = $28\, cm 	imes 26\, cm = 728\, cm^2$.Area of the circle = $\pi r^2 = 3.1416 	imes (10)^2 = 314.16\, cm^2$.Area of the shaded portion = $728 - 314.16 = 413.84\, cm^2 \approx 414\, cm^2$.Perimeter of the shaded portion = (Sum of the straight edges) + (Sum of the arc lengths of the four sectors).The straight edges are: $(28 - 10 - 10) + (28 - 10 - 10) + (26 - 10 - 10) + (26 - 10 - 10) = 8 + 8 + 6 + 6 = 28\, cm$.The four arcs form a full circle circumference: $2\pi r = 2 	imes 3.1416 	imes 10 = 62.832\, cm$.Total Perimeter = $28 + 62.832 = 90.832\, cm \approx 90.8\, cm$.

Find the perimeter and area of the shaded portion of the adjoining diagram.

Similar Questions

Find the perimeter (in $cm$) of a semicircle of radius $28\, cm$.

How many metres of cloth $5\, m$ wide will be required to make a conical tent,the radius of whose base is $7\, m$ and height is $24\, m ?$ (in $m$)

$A$ parallelogram has sides $60\, cm$ and $40\, cm$ and one of its diagonals is $80\, cm$ long. Its area is

An open box is made of wood $2\, cm$ thick. Its internal length is $86\, cm,$ breadth $46\, cm$ and height is $38\, cm.$ The cost of painting the outer surface of the box at $Rs.$ $10$ per $m^2$ is? (in $Rs.$)

If the diameter of each circle is $14 \, cm$ and $DC = CE$,find the area of $\Delta BDE$ in $cm^2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module