A glass vase weighs 0.61 lb. How much does a similarly shaped vase made of the same glass weigh if each dimension is 2 times as large? Explain.A. 2.44 lb; the vase dimensions are 2 times as large, so the weight is 4 times as much because 2sq = 4.B. 1.22 lb; the vase dimensions are 2 times as large, so double the weight.C. 9.76 lb; the vase dimensions are 2 times as large, so the weight is 16 times as much because 2sq4 = 16.D. 4.88 lb; the vase dimensions are 2 times as large, so the weight is 8 times as much because 2sq3 = 8.
Accepted Solution
A:
let x--------> volume of the small glass vase D------> density of the glass vase
we know that [volume of larger glass vase]=[scale factor]³*[volume of smaller glass vase] scale factor=2 [volume of larger glass vase]=[2]³*[x]-------> 8x units³
Density=mass / volume--------> mass =Density*Volume
the weight of the smaller glass vase=D*V-------> 0.61=D*x
the weight of the larger glass vase=D*8x-------> 8*[D*x] therefore the weight of the larger glass vase=8*[weight of the smaller glass vase] the weight of the larger glass vase=8*[0.61]------> 4.88 lb
the answer is the option D. 4.88 lb; the vase dimensions are 2 times as large, so the weight is 8 times as much because 2sq3 = 8