Poppy is visiting her Grandparents for half-term and has been treated to a small box of sweets.
The box of sweets is a cuboid and has sides of length 4cm, x cm and y cm.
The volume of the cuboid is 119 cm^3
The total surface area of the cuboid is 155.5 cm^2
Given that x is greater than y work out the value of x and the value of y.
Answer:
119 = 4 xy
4x = 119/y
x = 119/ (4y)
2 * (4x) + 2 * (xy) + 2 * (4y) = 155.50
Substituting in:
2 * 119/y + 2 * 119/(4y) * y + 8y = 155.50
Times all terms by y:
238 +59.5 y + 8 y^2 = 155.5 y
8y^2 -96y +238 = 0
4y^2 – 48y + 119 = 0
4 * 119 = 476
Factors:
2
2
17
7
Need to add up to 48:
2 x 17 = 34
2 x 7 = 14
(2y – 7) (2y – 17) = 0
2y = 7 or 2y = 17
y = 3.5 or 8.5
Substituting back in:
x = 119/ (4y)
Therefore:
x = 8.5 (if y = 3.5) or 3.5 (if y = 8.5)
As x > y
x = 8.5cm and y = 3.5cm