A copper wire when bent in the form of an equilateral triangle has an area of cm2. If the same wire is bent into the form of a circle, find the area enclosed by the wire.

Question

KnowledgeBoat · Accepted Answer

By formula, Area of equilateral triangle = (side)2 Given, Area of equilateral triangle = cm2 ⇒(side)2 = ⇒ (side)2 = 121 × 4 ⇒ (side)2 = 484 ⇒ side = ⇒ side = 22 cm. Perimeter of equilateral triangle = 3 x side = 3 x 22 = 66 cm. Circumference of circle of same wire = Perimeter of triangle of same wire Let radius of circle be r cm. ∴ 2πr = 66 ⇒ 2 × × r = 66 ⇒ 44 × r = 66 × 7 ⇒ r = ⇒ r = = 10.5 cm Area of circle = πr2 = × (10.5)2 = × 10.5 × 10.5 = 22 × 1.5 × 10.5 = 346.5 cm2. Hence, area = 346.5 cm2.

Mathematics

A copper wire when bent in the form of an equilateral triangle has an area of cm2. If the same wire is bent into the form of a circle, find the area enclosed by the wire.

Mensuration

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Mathematics

A copper wire when bent in the form of an equilateral triangle has an area of cm2. If the same wire is bent into the form of a circle, find the area enclosed by the wire.

Mensuration

Related Questions

The circumference of a circle exceeds its diameter by 180 cm. Calculate :(i) the radius(ii) the circumference and(iii) the area of the circle.

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The sum of the radii of two circles is 140 cm and the difference of their circumference is 88 cm. Find the radii of the two circles.

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The circumference of a circle exceeds its diameter by 180 cm. Calculate :
(i) the radius
(ii) the circumference and
(iii) the area of the circle.

A copper wire when bent in the form of a square encloses an area of 272.25 cm². If the same wire is bent into the form of circle, what will be the area enclosed by the wire?

The sum of the radii of two circles is 84 cm and the difference of their areas is 5544 cm². Calculate the radii of the two circles.