Question

Mateo wants to make a toy sailboat. He has two pieces of wood to choose from. His first piece of wood is a block that measures 18'' x 10" x 8". It weighs 46.65 lbs. His second piece of wood is a log of wood measuring 21" long, with an average circumference of 25.12". It weighs 39.25 lbs. The sailboat needs to float, but both blocks of wood are denser than wood usually is, and he's not sure either piece of wood will float. He doesn't want to get the water wet before he's applied a sealant, so he isn't willing to just drop them in the water to find out.
2a. Which common solid can he use to represent the block? Which common solid can he use to represent the log? (2 points)
2b. What is the density of the block in pounds per cubic inch? Give the formula for density and show your work. (3 points)
2c. What is the density of the log in pounds per cubic inch? Give the formula for density and show your work. Use 3.14 for π. (Hint: you can determine the radius from the circumference.) (3 points)
2d. Water has a density of about 0.0361 pounds/cubic inch. Anything rarer will float, and anything denser will sink. Which of the pieces of wood are suitable for making a toy boat that will float? (2 points)

Answer 1

Step-by-step explanation:

2a. The block of wood has the shape of a rectangular prism.  The log has the shape of a cylinder.

2b. Density is mass divided by volume.  We know the mass, but we need to find the volume.

Volume of a rectangular prism is:

V = whl

where w is the width, h is the height, and l is the length

V = (18)(10)(8)

V = 1440 in³

So the density is:

d = 46.65 lbs / 1440 in³

d = 0.0324 lb/in³

2c.  Volume of a cylinder is:

V = πr²h

where r is radius and h is height.

The circumference is C = 2πr, so r = C / (2π).

r = 25.12 / (2*3.14)

r = 4.00

V = 3.14 (4.00)² (21)

V = 1055.04 in³

So the density is:

d = 39.25 lb / 1055.04 in³

d = 0.0372 lb/in³

2d.  The block is less dense than water; the log is more dense than water.  So he should make the boat out of the block.