Question

question 5. naomi is building a circular coffee table for her living room. she needs to find the area of the top of the table that has a radius of ( 5 x ^ { \frac { 2 } { 3 } } y ^ { \frac { 3 } { 4 } } ) inches. the area of a circle can be found using ( a = pi r ^ { 2 } ). what is the area top of the coffee table? a. ( 25 pi x ^ { \frac { 9 } { 3 } } y ^ { \frac { 9 } { 4 } } ) b. ( 10 pi x ^ { \frac { 18 } { 8 } } y ^ { \frac { 8 } { 8 } } ) c. ( 15 pi x ^ { 9 } y ^ { 4 } ) d. ( 15 pi x ^ { 9 } y ^ { \frac { 3 } { 2 } } )

Explanation:

Step1: Substitute the radius into the area formula

The formula for the area of a circle is \(A = \pi r^{2}\). Given \(r = 5x^{\frac{3}{2}}y^{\frac{3}{4}}\), we substitute it into the formula: \(A=\pi(5x^{\frac{3}{2}}y^{\frac{3}{4}})^{2}\)

Step2: Expand the square

Using the power - of - a - product rule \((ab)^{n}=a^{n}b^{n}\) and the power - of - a - power rule \((a^{m})^{n}=a^{mn}\), we have:

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Answer:

A. \(25\pi x^{3}y^{\frac{3}{2}}\)