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Mathematics : asked on tammydunner32
 26.09.2020

Jerry wants to compare the volume of cones when the dimensions change. He states the volume of the cone is four times greater when the height and radius are doubled.

Explain the error in Jerry's reasoning.

Explain what happens to the volume of a cone if the height and also the radius are doubled.

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Step-by-step answer

03.11.2022, solved by verified expert
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Bhaskar Singh Bora
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Answer:

See detailed explanation below

Step-by-step explanation:

Error: volume of cone when dimensions are doubled is 8 times of the original cone.

Proof: 

Volume of cone V = πr²h/3 

V ∝ r²h (since π and 3 are constants) 

Let V1, r1 and h1 are the volume, radius and height of the first cone respectively.

And Let V2, r2 and h2 are the volume, radius and height of the second cone (with 2× dimensions of 1st cone i.e. r2 = 2r1 and h2 = 2h1) respectively.  

V2/V1 = (r1)²h1/(r2)²h2 

= (r1)²h1/(2r1)²(2h1)

= (r1)²h1/8(r1)²h1 

V2/V1 = 1/8

V2 = 8V1 

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Mathematics, 26.03.2020 20:52, mohammadhosseinkarim David is building wooden picture frames. Each frame requires 3/4 feet of wood. If David started with 12 feet of wood and now has 6 feet of wood remaining, how many pictures frames has he built?
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