Calculate the radius and the area of the brick region?

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Answer 1 · 2018-05-24T12:32:13

See a solution process below:

The diameter of the shaded area is the same as the height of the rectangular area: 30cm

The relationship between the radius and diameter of a circle is:

$d = 2 r$ $d = 2r$ or $r = \frac{d}{2}$ $r = d/2$

Substituting the diameter gives the radius as:

$r = \frac{30 cm}{2} = 15 cm$ $r = (30"cm")/2 = 15"cm"$

The RADIUS of the shaded area is: 15cm

The formula for the area of a circle is:

$A_{c} = π r^{2}$ $A_c = pir^2$

Substituting the radius from above and calculating the area gives:

$A_{c} = π \cdot {(15 cm)}^{2}$ $A_c = pi * (15"cm")^2$

$A_{c} = π \cdot 225 {cm}^{2}$ $A_c = pi * 225"cm"^2$

$A_{c} = 225 π {cm}^{2}$ $A_c = 225pi"cm"^2$

Or, using 3.14 to approximate $π$ $pi$ :

$A_{c} ≅ 225 \cdot 3.14 {cm}^{2}$ $A_c ~= 225 * 3.14"cm"^2$

$A_{c} ≅ 706.5 {cm}^{2}$ $A_c ~= 706.5"cm"^2$

The AREA of the shaded area is approximately 706.5 square centimeters