Advertisements
Advertisements
प्रश्न
If the perimeter of a semi-circular protractor is 36 cm, then its diameter is
पर्याय
10 cm
12 cm
14 cm
16 cm
उत्तर
We know that perimeter of a semi-circle of radius `r=1/2(2pir)+2r`.................(1)
We have given the perimeter of the semi-circle and we are asked to find the diameter of the semi-circle.
Therefore, substituting the perimeter of the semi-circle in equation (1) we get,
`36=1/2(2pi r)+2r`
Multiplying both sides of the equation by 2 we get,
`72=2pir+4r`
Substituting `pi=22/7` we get,
`72=2xx22/7 r+4r`
`∴ 72=44/7 r+4r`
Now we will multiply both sides of the equation by 7.
`504=44r+28 r`
Adding like terms we get,
`∴ 504=72 r`
Dividing both sides of the equation 72 we get, `r=7`
Therefore, radius of the semi circle is 7cm.
Now we will find the diameter.
Diameter=`2xxr`
∴ Diameter=`2xx7`
∴ Diameter=`14`
Hence, diameter of the semi-circle is `14 cm`
APPEARS IN
संबंधित प्रश्न
Find the area and perimeter of an isosceles right angled triangle, each of whose equal sides measure 10cm.
The area of rectangle is `192cm^2` and its perimeter is 56 cm. Find the dimensions of the rectangle.
ABCDEF is a regular hexagon with centre O (in the following figure). If the area of triangle OAB is 9 cm2, find the area of : (i) the hexagon and (ii) the circle in which the haxagon is incribed.
The diameter of a coin is 1 cm (in the following figure). If four such coins be placed on a table so that the rim of each touches that of the other two, find the area of the shaded region (Take π = 3.1416).
In the following figure, AB and CD are two diameters of a circle perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
In a hospital used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of hospital whose length is 25 m and breadth is 20 m. If tank is filled completely then what will be the height of standing water used for irrigating the park.
If the adjoining figure is a sector of a circle of radius 10.5 cm, what is the perimeter of the sector? (Take \[\pi = 22/7\])
If the radius of a circle is doubled, its area becomes ____________.
Is the area of the circle inscribed in a square of side a cm, πa2 cm2? Give reasons for your answer.
Area of a rectangle and the area of a circle are equal. If the dimensions of the rectangle are 14 cm × 11 cm, then radius of the circle is ______.
