Answer:
430. cm³
Explanation:
You want the volume of a cuboid with edge dimensions 5 cm and 7 cm, and space diagonal 15 cm.
Third edge
The square of the length of the space diagonal is the sum of the squares of the lengths of the cuboid edges. If x represents the third edge, we have ...
(5 cm)² +(7 cm)² +x² = (15 cm)²
x² = (225 -25 -49) cm² = 151 cm²
x = √151 cm
Volume
The volume of the cuboid is the product of its edge lengths:
V = LWH
V = (5 cm)(7 cm)(√151 cm) ≈ 430.09 cm³
Rounded to 3 significant figures, the cuboid volume is 430. cm³.
__
Additional comment
The decimal point in the number indicates the trailing zero is significant. Alternatively, we could write the volume as 4.30×10² cm³, showing 3 significant figures.
<95141404393>