An oblique candle with a volume of 270 cubic centimeters is 18 centimeters tall. The width of the triangular candle base is 5 centimeters, and the width of the slanted candle is 7 centimeters.

An oblique triangular prism has a volume of 270 cubic centimeters. The vertical height is 18 centimeters. The width of the triangular bases is 6 centimeters, and the width of the slanted prism is 7 centimeters.

What dimensions of the box are required to fit the candle?

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 = × 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 = (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

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