Final answer:
The height of the object with a volume of 162 units^3 and a base area of 81 units^2 is 2 units. For the triangle with a base of 166 mm and height of 930.0 mm, the area is 0.07719 m^2, expressed to the correct number of significant figures.
Step-by-step explanation:
To find the height of an object given the volume and the area of the base, you can use the formula V = Ah, where V is the volume, A is the area of the base, and h is the height. With a volume of 162 units3 and a base area of 81 units2, the height can be calculated by rearranging the formula to h = V / A. Plugging in the values gives us h = 162 / 81, which simplifies to h = 2 units.
In the case of the formula for the area of a triangle, A = 1/2 × base × height, if the base is 166 mm and the height is 930.0 mm, the area would be A = 1/2 × 166 mm × 930.0 mm. Calculated, the area equals A = 1/2 × 166 × 930.0 mm2 = 77,190 mm2. Converting to square meters (since there are 1,000,000 mm2 in 1 m2) and keeping the proper number of significant figures, we get A = 0.07719 m2.