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two circles of inscribed in a rectangle if the radius of the circle is 3cm what is the area inside the rectangle not occupied by the circle use - = 3.14​

Sagot :

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Answer:

Given:Radius of each circle, ( r = 3 ) cm

Step-by-step solution:Calculate the diameter of the circle:

1. Calculate the diameter of the circle:

[tex]d = 2r = 2 \times 3 = 6 \text{ cm}[/tex]

2. Width of the rectangle = diameter of one circle = 6 cm

Length of the rectangle

[tex]{= 2 \times diameter \: of \: one \: circle = 2 \times 6 = 12 \: cm}[/tex]

3. Area of the rectangle:

Area of Rectangle = length x width = 12 cm x 6 cm = cm²

4. Area of one circle:

= πr² = 3.14 x 3² = 3.14 x 9 = 28.26 cm²

5. Total area occupied by the two circles:

[tex]= 2 \times 28.26 \text{ cm}^2 = 56.52 \text{ cm}^2[/tex]

6. Area inside the rectangle not occupied by the circles:

Area not occupied = Area of the rectangle Total area of circles

[tex]72 \text{ cm}^2 - 56.52 \text{ cm}^2 = 15.48 \text{ cm}^2 [/tex]

Sailoreisceidn

[tex] \sf{The \: right \: answer \: is \: \boxed{15.48 cm²}}.[/tex]

[tex] \sf{A = \pi \times {r}^{2}}[/tex]

[tex] \sf{A \:= 3.14 \times {3}^{2}}[/tex]

[tex] \sf{A = 3.14 \times 9 = 28.26 \: {cm}^{2}} [/tex]

[tex] \sf{A = 2 \times 28.26 = 56.52 \: {cm}^{2}}[/tex]

[tex] \sf{Length \: of \: the \: rectangle = 2 \times 6 = 12 \: cm}[/tex]

[tex] \sf{Area \: of \: the \: rectangle = l \times w = 12 \: cm \times 6 \: cm = 72 \: {cm}^{2}}[/tex]

[tex] \sf{Area \: unoccupied \: by \: the \: circles = Area \: of \: the \: rectangle \: - Area \: of \: the \: two \: circle}[/tex]

[tex] \sf{A = 72 \: {cm}^{2} - 56.52 \: {cm}^{2}}[/tex]

[tex] \huge \sf \green{A = 15.48 \: {cm}^{2}}[/tex]

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