a cube of edge 5 centimeters is cut from a rectangular block wood as shown.find the volume of the remaining.12cm 15cm 5cm
AAAaannndd the bot gets it wrong yet again!
12*15*10 - 5^3 = 1675
To find the volume of the remaining rectangular block wood after a cube of edge 5 centimeters is cut out, we need to calculate the original volume of the block and subtract the volume of the cube.
Step 1: Calculate the original volume of the rectangular block wood.
The original volume of a rectangular block can be calculated using the formula: Volume = length x width x height.
Length = 12 cm
Width = 15 cm
Height = 5 cm
Volume = 12 cm x 15 cm x 5 cm
Volume = 900 cm^3
Step 2: Calculate the volume of the cube that was cut out.
The volume of a cube can be calculated using the formula: Volume = edge^3.
Edge = 5 cm
Volume of the cube = 5 cm x 5 cm x 5 cm
Volume of the cube = 125 cm^3
Step 3: Subtract the volume of the cube from the original volume of the block.
Volume of the remaining rectangular block wood = Original volume - Volume of the cube
Volume of the remaining rectangular block wood = 900 cm^3 - 125 cm^3
Volume of the remaining rectangular block wood = 775 cm^3
Therefore, the volume of the remaining rectangular block wood is 775 cm^3.
To find the volume of the remaining rectangular block wood after a cube is cut out, we need to subtract the volume of the cube from the original volume of the rectangular block.
Given:
The original dimensions of the rectangular block: 12 cm, 15 cm, 5 cm
The edge length of the cube: 5 cm
1. Calculate the volume of the rectangular block:
Volume_rectangular_block = Length x Width x Height
Volume_rectangular_block = 12 cm x 15 cm x 5 cm
Volume_rectangular_block = 900 cm³
2. Calculate the volume of the cube:
Volume_cube = Edge length x Edge length x Edge length
Volume_cube = 5 cm x 5 cm x 5 cm
Volume_cube = 125 cm³
3. Subtract the volume of the cube from the volume of the rectangular block to find the volume of the remaining wood:
Volume_remaining_wood = Volume_rectangular_block - Volume_cube
Volume_remaining_wood = 900 cm³ - 125 cm³
Volume_remaining_wood = 775 cm³
Therefore, the volume of the remaining rectangular block wood is 775 cm³.