The shape of the top of a table in a restaurant is that of a segment of a circle with centre O and ∠BOD = 90°. BO = OD = 60 cm. Find :
(i) the area of the top of the table;
(ii) the perimeter of the table.

Question

The shape of the top of a table in a restaurant is that of a segment of a circle with centre O and ∠BOD = 90°. BO = OD = 60 cm. Find :
(i) the area of the top of the table;
(ii) the perimeter of the table.

KnowledgeBoat · Accepted Answer

Since, OB = OD = 60 cm Thus, radius of circle (r) = 60 cm ∠BOD = 90 . (i) Area of circle = πr2 = 3.14 × (60)2 = 3.14 × 3600 = 11304 cm2. Area of sector of 90 = × πr2 = × 11304 = 2826 cm2. From figure, Area of top of the table = Area of circle - Area of sector 90 Area of top of the table = 11304 - 2826 = 8478 cm2. Hence, area of top of the table = 8478 cm2. (ii) Circumference of circle = 2πr = 2 × 3.14 × 60 = 376.8 cm. Length of 270 arc = × 376.8 = × 376.8 = 3 × 94.2 = 282.6 cm. From figure, Perimeter of table top = Circumference of major arc (of 270 ) + OB + OD = 282.6 + 60 + 60 = 282.6 + 120 = 402.6 cm. Hence, perimeter of the table = 402.6 cm.

Mathematics

The shape of the top of a table in a restaurant is that of a segment of a circle with centre O and ∠BOD = 90°. BO = OD = 60 cm. Find :
(i) the area of the top of the table;
(ii) the perimeter of the table.

Mensuration

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Mathematics

The shape of the top of a table in a restaurant is that of a segment of a circle with centre O and ∠BOD = 90°. BO = OD = 60 cm. Find :(i) the area of the top of the table;(ii) the perimeter of the table.

Mensuration

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The shape of the top of a table in a restaurant is that of a segment of a circle with centre O and ∠BOD = 90°. BO = OD = 60 cm. Find :
(i) the area of the top of the table;
(ii) the perimeter of the table.

In the given figure, ABCD is a square of side 5 cm inscribed in a circle. Find :
(i) the radius of the circle,
(ii) the area of the shaded region.

In the given figure, ABCD is a rectangle inscribed in a circle. If two adjacent sides of the rectangle be 8 cm and 6 cm, calculate :
(i) the radius of the circle; and
(ii) the area of the shaded region.