an action hero needs to replace a valuable artifact with a pile of sand of equal mass within 5 seconds, otherwise a trapdoor opens and she falls into a pit of slimy slugs. The artifact and two of its measurements are shown in the following image - dimensions of said image below
9.5 cm width
38.1 height
She assumes the artifact is made of limestone, which has a density of 2.71 g/cm^3. She plans to quickly replace the artifact with a pile of sand of equal mass. Sand has a density of 1.6 g/cm^3.
A. What common three-dimensional figure best models the artifact?
B.To the nearest tenth of a cm^3, what is the volume of the three-dimensional figure you chose?
C. Use your answer to part B and the formula density= mass/volume to estimate the mass of the artifact
Estimate the volume of the sand she should use to replace the artifact
and how on earth would I know what shape it is?
it is a rectangle
Its a picture of one of those easter island statues
A. To determine the common three-dimensional figure that best models the artifact, we can use the given dimensions. The first thing we can determine is the shape's cross-sectional area, which in this case would be a rectangle with dimensions of 9.5 cm by 38.1 cm.
B. The volume of the three-dimensional figure can be found by multiplying the cross-sectional area by the height of the shape. Therefore, the volume is given by:
Volume = cross-sectional area * height
Volume = (9.5 cm * 38.1 cm) * height
The artifact's height is not given, so we cannot calculate the exact volume of the artifact. However, we can assume that it is a rectangular solid and use the given dimensions as an estimation. If, for example, the height of the artifact is 5 cm, the volume would be:
Volume = (9.5 cm * 38.1 cm) * 5 cm
To find the volume to the nearest tenth of a cm^3, we can calculate it using these dimensions.
C. To estimate the mass of the artifact, we can use the formula:
Density = mass / volume
Rearranging the formula, we get:
Mass = density * volume
Using the given density of limestone as 2.71 g/cm^3 and the volume we calculated in part B, we can estimate the mass of the artifact.
To estimate the volume of sand needed to replace the artifact, we need to find a volume that has the same mass as the artifact. Since the density of sand is given as 1.6 g/cm^3, we can use the formula:
Mass = density * volume
To find the volume of sand needed, we rearrange the formula:
Volume = mass / density
Substituting the estimated mass of the artifact and the density of sand into the formula, we can estimate the volume of sand needed.