1. The radius of a cone whose radius and height are equal, a hemisphere, a cylinder whose radius and height are equal and a sphere are 'r'. Prove that
their volumes are in arithmetic sequence.
their volumes are in arithmetic sequence.
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Step-by-step explanation:
volume of cone=1/3*pi*r^2*h=1/3*pi*r^3
volume of hemisphere=2/3*pi*r^3
volume of cylinder=pi*r^2*h=pi*r^3
hence proved....
there are in arithmetic sequence
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Answer:
radius = r , height = r
V (cone) = 1/3*pi*r²*r = 1/3*pi*r³
V (hemisphere) = 2/3*pi*r³
V (cyl) = pi*r²*r = pi*r³
V (sphere) = 4/3*pi*r³
V(cone) : V(hemi) : V(cyl) : V(sphere)
= 1/3*pi*r³ : 2/3*pi*r³ : pi*r³ : 4/3*pi*r³
=> 1/3 : 2/3 : 1 : 4/3
=> 1/3 , 2/3, 1, 4/3 are in A.P with d = 1/3
=> 1/3, (1/3+1/3) , (1/3 + 2*1/3), (1/3 + 3*1/3)
=> a, (a + d) , (a + 2d), a + 3d)