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URGENT PLEASE

The diagram shows a triangular prism.

8cm

15 cm

17cm

The total surface area of the prism is 600 cm²

Work out the volume of the prism.

URGENT PLEASE The diagram shows a triangular prism 8cm 15 cm 17cm The total surface area of the prism is 600 cm² Work out the

Answer :

Final answer:

The volume of the triangular prism, given the base dimensions and total surface area, is calculated by first determining the height of the prism using the total surface area, base area and perimeter of the base, then using this height to calculate volume. The volume is found to be 720 cm³.

Explanation:

In this case, we are asked to find the volume of a triangular prism. Firstly, we can find the base area (A) of the triangular prism using the formula for area of a right triangle, which is A = 1/2 * base * height; using the given dimensions, we have A = 1/2 * 8cm * 15cm = 60 cm². Volume (V) of the prism is given by V = A * h, where A is the base area and h is the height. Now, given that the Surface area (S) of a prism = 2 * A + p * h, where p is the perimeter of the base, we can rearrange for h to get h = (S - 2A) / p. Substituting the given total surface area (S = 600 cm²), base area (A = 60 cm²), and perimeter (p = 8cm+15cm+17cm = 40cm), we get h = (600 - 120) / 40 = 12cm. Therefore, the volume of the prism is V = 60 cm² * 12 cm = 720 cm³.

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Rewritten by : Barada

The total surface area of a triangular prism can be found using the formula:

SA = 2B + Ph

where:

B is the area of the base

P is the perimeter of the base

h is the height of the prism

In this case, we are given that the total surface area is 600 cm², and the three dimensions of the prism are 8 cm, 15 cm, and 17 cm.

To find the volume of the prism, we can use the formula:

V = Bh

where B is the area of the base and h is the height of the prism.

First, we need to find the area of the base. The base is a triangle with sides 8 cm, 15 cm, and 17 cm. We can use Heron's formula to find the area of this triangle:

s = (8 + 15 + 17)/2 = 20

Area of triangle = √(20(20-8)(20-15)(20-17)) ≈ 60.31 cm²

Next, we need to find the height of the prism. We can use the formula for surface area to find the height:

SA = 2B + Ph

600 = 2(60.31) + (8 + 15 + 17)h

600 = 120.62 + 40h

40h = 479.38

h ≈ 11.98 cm

Finally, we can use the formula for volume to find the volume of the prism:

V = Bh

V = (60.31)(11.98)

V ≈ 723.5 cm³

Therefore, the volume of the triangular prism is approximately 723.5 cm³.