Answer:
The dimensions of the box are 6 cm , 7 cm , 18 cm
Step-by-step explanation:
The formula of the volume of the candle is V = Base area × height
∵ The volume of the candle is 270 cm³
∴ V = 270
∵ The candle is 18 cm tall
∴ Its height = 18 cm
- Substitute the values of V and the height in the formula of
the volume above
∴ 270 = base area × 18
- Divide both sides by 18 to find the base area
∴ 15 = base area
∴ The area of the base of the candle is 15 cm²
The formula of the area of a triangle is A = [tex]\frac{1}{2}[/tex] × b × h
∵ The base is shaped a triangle with 5 cm
∴ b = 5
∵ Its area is 15 cm²
∴ A = 15
- Substitute this value in the formula of the area to find h
∴ 15 = [tex]\frac{1}{2}[/tex] (5) h
- Multiply both sides by 2
∴ 30 = 5 h
- Divide both sides by 5
∴ 6 = h
∴ The height of the base is 6 cm
∵ The width of the slanted candle is 7 centimeters
∴ The dimensions of the box are 6 cm , 7 cm , 18 cm
