Question

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.​

Answer 1

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 2

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)