What is 2pi(2a+(8a)/(3pi))(1/4 pia^2) ?

The solution to 2pi(2a+(8a)/(3pi))(1/4 pia^2) is (pi(3pi+4)a^3)/3

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simplify 2pi(2a+(8a)/(3pi))(1/4 pia^2)

simplify

2 π (2 a + \frac{8 a}{3 π}) (\frac{1}{4} π a^{2})

\frac{π ( 3 π + 4 ) a ^{3}}{3}

Solution steps

2 π (2 a + \frac{8 a}{3 π}) (\frac{1}{4} π a^{2})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

ππ = π^{1 + 1}

= 2 (2 a + \frac{8 a}{3 π}) \frac{1}{4} π^{1 + 1} a^{2}

Add the numbers:

1 + 1 = 2

= 2 (2 a + \frac{8 a}{3 π}) \frac{1}{4} π^{2} a^{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2 ( 2 a + \frac{8 a}{3 π} ) π ^{2} a ^{2}}{4}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2 π ^{2} a ^{2} ( 2 a + \frac{8 a}{3 π} )}{4}

Cancel the common factor:

2

= \frac{π ^{2} a ^{2} ( 2 a + \frac{8 a}{3 π} )}{2}

Join

2 a + \frac{8 a}{3 π} : \frac{6 πa + 8 a}{3 π}

= \frac{π ^{2} \frac{6 πa + 8 a}{3 π} a ^{2}}{2}

Multiply

π^{2} a^{2} \frac{6 aπ + 8 a}{3 π} : \frac{π a ^{2} ( 6 πa + 8 a )}{3}

= \frac{\frac{π a ^{2} ( 6 πa + 8 a )}{3}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π a ^{2} ( 6 πa + 8 a )}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{π a ^{2} ( 6 πa + 8 a )}{6}

Factor

π a^{2} (6 πa + 8 a) : 2 π (3 π + 4) a^{3}

= \frac{2 π ( 3 π + 4 ) a ^{3}}{6}

Cancel the common factor:

2

= \frac{π ( 3 π + 4 ) a ^{3}}{3}

2 (200 e^{- \frac{463}{100}}) 40.75

e e^{0}

e e^{1}

(r^{2} sin^{2} (θ)) (2 r^{2} sin (θ))

(y^{2} - 4) (y^{2} - 4)

What is 2pi(2a+(8a)/(3pi))(1/4 pia^2) ?
The solution to 2pi(2a+(8a)/(3pi))(1/4 pia^2) is (pi(3pi+4)a^3)/3