Question

Q9. A triangular prism has a volume of 480 cm³. The cross section of the prism is an isosceles triangle with base 6 cm. The depth of the prism is 20 cm. Find the length of the longest side of the triangular cross section. (Answer correct to 2 d.p.)​

Answer 1

Step 1: The volume of a prism is determined by the area of the cross section multiplied by the height of the prism.

Step 2: The area of an isosceles triangle can be calculated by A = (base x height)/2.

Step 3: Substituting values, we get A = (6 cm * h)/2.

Step 4: Since the volume of the triangular prism is 480 cm3, substituting in the formula V = A * height, we get 480 cm3 = (6 cm * h)/2 * 20 cm.

Step 5: Solving for h, we get h = 16 cm.

Step 6: Since it is an isosceles triangle, the longest side of the cross section is also 16 cm.

Answer: The length of the longest side of the triangular cross section is 16 cm.