The volumes of two similar cones are \(36\pi \, \text{cm}^3\) and \(288\pi \, \text{cm}^3\). The base radius of the smaller cone is 3 cm. Calculate the base radius of the larger cone.
Answer (2)
V 1 = 36 π c m 3 V 2 = 288 π c m 3 V 1 V 2 = k 3 ( k − s imi l a r sc a l e ) k 3 = 36 π 288 π k 3 = 8 k = 3 8 k = 2
t h e ba se r a d i u s o f t h e s ma ll er co n e i s 3 c m t h e ba se r a d i u s o f t h e bi gg er co n e i 2 ⋅ 3 c m = 6 c m
The base radius of the larger cone is found to be 6 cm by using the ratio of the volumes of the similar cones. Given the volumes 36 π cm 3 and 288 π cm 3 , we calculated the scale factor of the dimensions. The smaller cone's base radius of 3 cm scales up by a factor of 2, resulting in the larger cone's base radius of 6 cm.
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