Question

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.

Answer 1

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