Question

21. a) A wooden block is formed in the shape shown by cutting a right rectangular solid from a larger one. What is the volume of the block?b) Check your calculations by using a second method to solve the problem.

Answer 1

Given:

A wooden block with a rectangular hollow

To Determine: The volume of the given wooden block

The wooden block as the shape of a cuboid

THe volume of a cuboid is given by the formula

`V_{\text{cuboid}}=l* w* h`

The volume of given woodem block is the total volume of the shape minus the volume of hollow

The dimension of the whole cuboid without the hollow is

`\begin{gathered} l=16cm \\ w=10cm \\ h=10cm \end{gathered}`

The dimension of the hollow is

`\begin{gathered} l=6cm \\ w=10cm \\ h=5cm \end{gathered}`

The volume of the wooden block would be

`\begin{gathered} V_{\text{wooden block}}=(16cm*10cm*10cm)-(6cm*10cm*5cm) \\ V_{\text{wooden block}}=1600cm^3-300cm^3 \\ V_{\text{wooden block}}=1300cm^3 \end{gathered}`

b) Calculate the volume using a second method

To use a second method, we would divide the cuboid into 3 different cuboid

Therefore, the volume of wooden block would be

`\begin{gathered} V_{\text{wooden block}}=V_a+V_b+V_c \\ Va=(5cm*10cm*10cm)=500cm^3 \\ V_b=(6cm*10cm*5cm)=300cm^3 \\ V_c=(5cm*10cm*10cm)=500cm^3 \\ V_{\text{wooden block}}=500cm^3+300cm^3+500cm^3 \\ V_{\text{wooden block}}=1300cm^3 \end{gathered}`

Hence, the volume of wooden block is the same for (a) and (b) using the second method as 1300cm³