Spanish mahogany has a density of 53lb/ft^3. What is the approximate weight (in pounds) of a piece of mahogany that measured 10in x 12in x 14in?
mass = volume x density
The density is given. The volume can be calculated from 10 x 12 x 14 which gives you the volume in cubic inches. You must then change this to cubic feet. There are 1728 cubic inches in a cubic foot. Post your work if you get stuck.
To calculate the weight (in pounds) of a piece of mahogany, you need to multiply its volume by its density.
1. First, calculate the volume of the piece of mahogany. The volume formula is V = l x w x h, where l is the length, w is the width, and h is the height.
V = 10in x 12in x 14in = 1680 in³
2. Next, convert the volume from cubic inches to cubic feet. Since 1 cubic foot = 12 inches x 12 inches x 12 inches = 1728 in³, divide the volume by 1728:
1680 in³ / 1728 in³/ft³ ≈ 0.9722 ft³
3. Finally, multiply the volume in cubic feet by the density of the mahogany to find the weight:
Weight = 0.9722 ft³ x 53 lb/ft³ ≈ 51.5006 lb
Therefore, the approximate weight of the piece of mahogany is about 51.5006 pounds.
To determine the weight of the piece of mahogany, you can use its density and volume. Density is defined as mass per unit volume. Therefore, to find the weight (mass) of the piece of mahogany, you need to calculate its volume first.
To find the volume of a rectangular cuboid (as in this case), you multiply its three dimensions: length, width, and height.
Volume = length x width x height
Given measurements:
Length = 10 inches
Width = 12 inches
Height = 14 inches
Volume = 10 inches x 12 inches x 14 inches
Now that you have the volume of the piece of mahogany, you can calculate its weight by multiplying the volume by the density.
Weight = Volume x Density
Given density: 53 lb/ft^3
However, the volume we obtained earlier is in cubic inches, so we need to convert it into cubic feet. Since there are 1728 cubic inches in a cubic foot (12 x 12 x 12), we divide the volume by 1728 to get the volume in cubic feet.
Volume (cubic feet) = Volume (cubic inches) / 1728
Weight = (Volume (cubic feet) x Density)
Following these steps:
Volume = 10 inches x 12 inches x 14 inches = 1680 cubic inches
Volume (cubic feet) = 1680 cubic inches / 1728 = 0.9722 cubic feet
Weight = 0.9722 cubic feet x 53 lb/ft^3 = 51.48 pounds
Therefore, the approximate weight of the piece of Spanish mahogany is approximately 51.48 pounds.