Question

Duing the last winter carnival the local college students built a 30-foot snowman out of 100 tons of snow. How much snow will be needed to build a 36-foot snowman this year/

Answer 1

Well, it's not clear if the snowman scales by getting taller but no wider or deeper, or scales in all three linear dimensions, or something more like the BMI scale where weight scales in proportion to the square of linear dimension.

The weight of the snow is proportional to the volume. Let's assume the snowman scales in all three dimensions so we use the third power.

$W = 100 \times \left(\dfrac{36}{30}\right)^3 = 100(\frac 6 5)^3 = 172.8 \textrm{ tons of snow}$