A cone and a pyramid have equal heights and volumes. If the base area of the pyramid is 154cm^2, find the radius of the cone

Radius = 8.575 cm Step-by-step explanation: Formula for volume of a pyramid is; V_p = ½Ah Where A is area of base and h is height Also, formula for volume of cone is given as; V_c = ⅓πr²h Now, we are told that V_p = V_c and that h is the same for both shapes. Thus ; ½Ah = ⅓πr²h h will cancel out to give; ½A = ⅓πr² Cross multiply to give; 3A/2π = r² Base area of pyramid is given as 154 cm². Thus; (3 × 154)/2π = r² r = √((3 × 154)/2π r = 8.575 cm

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