Joe is making a toy from a rectangular block of wood. He drills two holes, each with diameter 1.4 cm, through the block. The block of wood has length 15 cm, width 8 cm, and height 5 cm.
a)What is the volume of the block before the holes are drilled?
b)What is total volume removed by the drilled holes?
c)What is the volume of the block after the holes are drilled?
I honestly don't know how to set this up.
a) the block was (15)(8)(5) cm^3 = .....
you have to know the volume of a cylinder , which is
v = π r^2 h
You don't say in which direction the holes are drilled, so I can't continue
To solve this problem, we need to calculate the volume of the block of wood before the holes are drilled, the total volume removed by the drilled holes, and the volume of the block after the holes are drilled.
a) To find the volume of the block before the holes are drilled, we can use the formula for the volume of a rectangular prism:
Volume = length x width x height
Given:
Length = 15 cm
Width = 8 cm
Height = 5 cm
Substituting the values into the formula, we can calculate:
Volume = 15 cm x 8 cm x 5 cm = 600 cm³
So, the volume of the block before the holes are drilled is 600 cm³.
b) To find the total volume removed by the drilled holes, we need to calculate the volume of each hole and then multiply it by the number of holes drilled.
The formula for the volume of a cylinder is:
Volume = π x radius² x height
Given:
Diameter of the hole = 1.4 cm
Radius of the hole = 1.4 cm / 2 = 0.7 cm
Assuming the height of each hole is equal to the height of the block (5 cm), we can calculate the volume of each hole:
Volume of one hole = π x (0.7 cm)² x 5 cm = 9.15 cm³ (rounded to two decimal places)
Since two holes were drilled, we multiply the volume of one hole by 2:
Total volume removed by the drilled holes = 2 x 9.15 cm³ = 18.3 cm³ (rounded to one decimal place)
So, the total volume removed by the drilled holes is 18.3 cm³.
c) To find the volume of the block after the holes are drilled, we subtract the total volume removed by the drilled holes from the volume of the block before the holes were drilled:
Volume of block after drilling = Volume of block before drilling - Total volume removed by drilled holes
= 600 cm³ - 18.3 cm³
= 581.7 cm³ (rounded to one decimal place)
So, the volume of the block after the holes are drilled is 581.7 cm³.