Question

A wooden log has a diameter of 10 feet and a height of 3 feet.

a) Find the Surface Area of the log, to the nearest hundredth.
b) Find the density of the wood, to the nearest hundredth, if it weighs 504.20 pounds.
a) ______ square feet
b) ______ pounds/cubic foot

Answer 1

The surface area and density of a wooden log can be calculated using the formulae for a cylinder's area and volume along with the given dimensions and weight.

Step-by-step explanation:

The surface area of a cylindrical log can be found by adding the areas of the two circular ends and the rectangular wrap around the side. The formula for the surface area of a cylinder is A = 2πr^2 + 2πrh, where r is the radius and h is the height. Using the log's diameter of 10 feet (radius of 5 feet) and height of 3 feet, we calculate the surface area to the nearest hundredth.

The density of the wood can be determined using the formula ρ = m/V, where m is the mass and V is the volume. The volume of the log is found via the formula for the volume of a cylinder, V = πr^2h. Given the weight of 504.20 pounds, we can calculate the density in pounds per cubic foot, to the nearest hundredth.