We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
45
1
avatar

Two congruent cylinders each have radius 8 inches and height 3 inches. The radius of one cylinder and the height of the other are both increased by the same nonzero number of inches. The resulting volumes are equal. How many inches is the increase? Express your answer as a common fraction.

 Oct 13, 2019

Best Answer 

 #1
avatar
+2

Two congruent cylinders each have radius 8 inches and height 3 inches. The radius of one cylinder and the height of the other are both increased by the same nonzero number of inches. The resulting volumes are equal. How many inches is the increase? Express your answer as a common fraction.

 

Zwei kongruente Zylinder haben jeweils einen Radius von 8 Zoll und eine Höhe von 3 Zoll. Der Radius eines Zylinders und die Höhe des anderen Zylinders werden um die gleiche Anzahl von Zoll ungleich Null erhöht. Die resultierenden Volumina sind gleich. Wie viel Zoll ist die Zunahme? Drücken Sie Ihre Antwort als gemeinsamen Bruch aus.

 

\(V=h\pi r^2=h\pi r^2\\ V_2 =3''\cdot (8''+x)^2=(3''+x)\cdot (8'')^2\\ 3\cdot (64+16x+x^2)=192+64x\\ 192+48x+3x^2-192-64x=0\)

\(3x^2-16x=0\)

\(x_1=0\\ 3x_2=16\\ \color{blue}x_2=5\frac{1}{3}\)

\(5\frac{1}{3}\ inches\ is\ the\ increase.\)

laugh  !

asinus

 Oct 13, 2019
edited by asinus  Oct 13, 2019
 #1
avatar
+2
Best Answer

Two congruent cylinders each have radius 8 inches and height 3 inches. The radius of one cylinder and the height of the other are both increased by the same nonzero number of inches. The resulting volumes are equal. How many inches is the increase? Express your answer as a common fraction.

 

Zwei kongruente Zylinder haben jeweils einen Radius von 8 Zoll und eine Höhe von 3 Zoll. Der Radius eines Zylinders und die Höhe des anderen Zylinders werden um die gleiche Anzahl von Zoll ungleich Null erhöht. Die resultierenden Volumina sind gleich. Wie viel Zoll ist die Zunahme? Drücken Sie Ihre Antwort als gemeinsamen Bruch aus.

 

\(V=h\pi r^2=h\pi r^2\\ V_2 =3''\cdot (8''+x)^2=(3''+x)\cdot (8'')^2\\ 3\cdot (64+16x+x^2)=192+64x\\ 192+48x+3x^2-192-64x=0\)

\(3x^2-16x=0\)

\(x_1=0\\ 3x_2=16\\ \color{blue}x_2=5\frac{1}{3}\)

\(5\frac{1}{3}\ inches\ is\ the\ increase.\)

laugh  !

asinus

Guest Oct 13, 2019
edited by asinus  Oct 13, 2019

8 Online Users

avatar