MATH

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A sphere has five times the volume of a right cone that has a radius of 4.6 cm and a height of 7.7 cm. Determine the radius of the sphere to the tenth of a centimetre.

This question is multiple choice and these were the options:

A. 2.2cm
B. 3.4cm
C. 5.9cm
D. 9.3cm

I was sure it would be 5.9 cm, but I got that marked as incorrect.

This is how I got that answer.

I found the volume of the right cone and got 170.5 cm. Then I times that by 5 and got the volume of the sphere which is 852.5 cm. The formula for the sphere is 4/3*3.14*r^3. So I divided 4 by 3 and times that by 3.14. And I got 4.186666667. Then I divided 852.5/4.186666667 and I got 203.6225114. Then I triple rooted that and got 5.88 which I rounded off to 5.9. What am I doing wrong?

  • MATH -

    vol of cone = (1/3)π(4.6^2)(7.7) = 170.62 (you had that)

    so volume of sphere = 853.1099

    (4/3)πr^3 = 853.1099
    r^3 = 3(853.1099)/(4π) = 203.665
    r = cuberoot(50.91625) = 5.88 or their answer of 5.9


    check:
    sphere: V = (4/3)π(5.88^3) = 853.1099
    cone = 170.62
    and 853.1099/170.62 = 5.00005 , not bad!

    You are correct, They are wrong!

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