For questions 1–2, find the volume of the given prism. Round to the nearest tenth if necessary. 1. (1 point) 265.1 cm3 274.4 cm3 274.6 cm3 269.3 cm3 2. (1 point) 2,028.0 yd3 1,756.3 yd3 1,434.0 yd3 3,512.6 yd3 3

1. The answer is 269.3 cm³.

The volume of a the rectangular prism (V) is the product of its length (l), width (w), and height (h):
V = l * w * h

According to the image:
l = 12.1 cm
w = 5.3 cm
h = 4.2 cm

Therefore,
V = 12.1 * 5.3 * 4.2 = 269.3 cm³

2. The answer is 1,756.3 yd³.

The volume of the triangular prism (V) is:
V = 1/4 * h √(a⁴ + 2(ab)² + 2(ac)² * b⁴ + 2(bc)² * c⁴)
where: h - height of the prism,
a, b, c - sides of the base

According to the image:
h = 24 yd
a = b = c = 13 yd

Therefore:
V = 1/4 * 24 * √(13⁴ + 2(13 * 13)² + 2(13 * 13)² * 13⁴ + 2(13 * 13)² * 13⁴)
V = 1756.3 yd³

raphealnwobi raphealnwobi · Answer 2 · 2022-01-21T14:08:59+01:00

The volume of the prism is 269.3 cm³ and 1756.3 yd³

Volume

Volume shows the amount of space enclosed by a closed surface. It is the amount of space that an object occupies, or that is enclosed within a container.

1)

volume of prism = length * width * height
Volume = 12.1 * 5.3 * 4.2 = 269.3 cm³

2)

volume of triangular prism = 1756.3 yd³

The volume of the prism is 269.3 cm³ and 1756.3 yd³

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