A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $60$ and the height of the cylinder is $15$ . If the volume of the solid is $70 pi$ , what is the area of the base of the cylinder?

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A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $60$ and the height of the cylinder is $15$ . If the volume of the solid is $70 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-08-26T16:06:34

$"Area of Base of cylinder"=2pi$

Explanation:

$"The Diagram:"$

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$color(blue)("We know that the volume of the whole solid is"$ $70pi$

$(or)$

$color(red)("The sum of the volumes of the cone and cylinder is "$ $70pi$

$"Now lets set up an equation for solving the question"$

$color(brown)("Volume of cone"=1/3 pir^2h=v_1$

$color(brown)("Volume of cylinder"=pir^2h=v_2$

$"(Where "h" is the height and "r" is the radius)"$

$"Known values of the variables":$

$color(violet)(h$ $color(violet)("of"$ $color(violet)(v_1=60$

$color(violet)(h$ $color(violet)("of"$ $color(violet)(v_2=15$

$"We need to find the value of"$ $pir^2$ $"which is the base"$

$:.color(orange)(v_1+v_2=70pi$

$rarr1/3pir^2h+pir^2h=70pi$

$rarr1/3pir^(2)60+pir^(2)15=70pi$

$rarr1/cancel3^1pir^(2)cancel60^20+pir^(2)15=70pi$

$rarrpir^(2)20+pir^(2)15=70pi$

$"Rewrite the equation"$

$rarr20pir^(2)+15pir^(2)=70pi$

$rarr35pir^2=70pi$

$rarrpir^2=(cancel70^2pi)/cancel35^1$

$rArrcolor(green)(pir^2=2pi$

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A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $60$ and the height of the cylinder is $15$ . If the volume of the solid is $70 pi$ , what is the area of the base of the cylinder?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is 60 60 and the height of the cylinder is 15 15 . If the volume of the solid is 70 pi70 pi, what is the area of the base of the cylinder?

1 Answer

Explanation:

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A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $60$ and the height of the cylinder is $15$ . If the volume of the solid is $70 pi$ , what is the area of the base of the cylinder?