Work out the volume of the prism in cm^3 give your answer correct to 3 significant figures

The volume of the prism is 243 cm³

Step-by-step explanation:

The volume of the prism is V = B × H, where

∵ The prism is a triangular prism

∴ Its base is a triangle

∵ The base of it is a right triangle

∴ Its area B = b h, where b and h are the legs of the right angle

→ We have one leg of the right angle and the hypotenuse, so we

   must use the Pythagoras Theorem to find the other leg

∵ (5.4)² + h² = (7.8)²

∴ 29.16 + h² = 60.84

→ subtract 29.16 from oth sides

∴ h² = 31.68

→ Take √  for both sides

∴ h = 5.6284989 cm

→ Now find the area of the base

∵ B = (5.4)(5.6284989)

∴ B = 15.196947 cm²

→ Let us use the rule of the volume above

∵ V = B × H

∵ H = 16 cm

∴ V = 15.196947 × 16

∴ V = 243.151153 cm³

→ Round it to 3 significant figures

∴ V = 243 cm³

∴ The volume of the prism is 243 cm³

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step-by-step explanation: