# A solid hemisphere has a radius of x. A solid Cone has a diameter of 3x and a perpendicular height of y. the hemisphere and the cone have equal volumes. Show that y=8/9x. Use the formulas provided. Need help asap please!?

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### Sohini Khan

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The volume of a cone is r^2(pi)h/3. The volume of a hemisphere is 2(pi)r^3/3 - this is found by dividing the volume of a sphere by 2. If the volumes of both shapes are equal, we can say: (1.5x)^2(pi)(y)/3 = 2(pi)(x^3)/3 We can get rid of the pi on both sides, and multiply both sides by 3 as well, to simplify the equation. y(1.5x)^2 = 2x^3 Expanding the left side’s brackets gives us: 2.25yx^2 = 2x^3 Solving for y gives us: y = 2/2.25 * x^3/x^2 y = 8/9 * x y = 8/9x as required Hope that helps, ~ Sohini

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