A rectangular sheet measuring 80cm and 50cm is 2mm thick and is made of metal whose density is 2.5g/cm cubed.A square of side 5cm is removed from each corner of the rectangle & the remaining part folded to form an open cuboid.
Calculate
a)The area of metal that forms the
cuboid??
b)Mass of the empty cuboid in kg???
cuboid??
remaining area
= 80*50-4*(5*5)
=400-100
= 300 sq cm
Mass = density*volume
Density of metal = 2.5 g/cm³
Volume=300 sq cm *2mm
=300*0.2 cm³
=60 cm³
So mass of open box?
1950
To calculate these values, we need to follow a step-by-step process.
a) First, we need to calculate the area of the metal that forms the cuboid.
To do this, we need to determine the dimensions of the cuboid after cutting the squares from the corners.
The length and width of the remaining part of the rectangle will be reduced by twice the side length of the cut square (5 cm).
The new length of the cuboid is: 80 cm - 2 * 5 cm = 80 cm - 10 cm = 70 cm.
The new width of the cuboid is: 50 cm - 2 * 5 cm = 50 cm - 10 cm = 40 cm.
The thickness of the cuboid remains the same at 2 mm or 0.2 cm.
The area of the metal that forms the cuboid is the product of its length, width, and height:
Area = Length * Width * Thickness
= 70 cm * 40 cm * 0.2 cm
b) To calculate the mass of the empty cuboid, first, we need to calculate its volume. The volume of a cuboid is the product of its length, width, and height:
Volume = Length * Width * Thickness
= 70 cm * 40 cm * 0.2 cm
We then need to convert the cubes of cm to cubes of meters to obtain the volume in cubic meters:
Volume (in cubic meters) = Volume (in cubic cm) / (100 cm / 1 meter)^3
To convert the density from grams per cubic centimeter to kilograms per cubic meter, we divide the density by 1000 (as there are 1000 grams in a kilogram):
Density (in kg/m³) = Density (in g/cm³) / 1000
Finally, we can calculate the mass using the formula:
Mass = Volume * Density
c) To express the answer for the mass of the empty cuboid in kilograms, divide the mass by 1000 (as there are 1000 kilograms in a metric ton).
To solve this problem, we need to follow a few steps:
Step 1: Calculate the volume of the original rectangular sheet.
Step 2: Calculate the volume of the removed squares.
Step 3: Subtract the volume of the removed squares from the volume of the original rectangular sheet to find the volume of the remaining part.
Step 4: Calculate the area of the metal that forms the cuboid using the dimensions of the remaining part.
Step 5: Calculate the mass of the empty cuboid.
a) Calculation of the area of metal that forms the cuboid:
Step 1: Calculate the volume of the original rectangular sheet.
Volume = Length x Width x Height
Volume = 80 cm x 50 cm x 0.2 cm (since 2 mm = 0.2 cm)
Volume = 800 cm³
Step 2: Calculate the volume of the removed squares.
Volume of one square = Length x Width x Height
Volume of one square = 5 cm x 5 cm x 0.2 cm
Volume of one square = 5 cm³
As we are removing two squares (one from each corner), the total volume of the removed squares is 2 x 5 cm³ = 10 cm³.
Step 3: Calculate the volume of the remaining part.
Volume of the remaining part = Volume of the original rectangular sheet - Volume of the removed squares
Volume of the remaining part = 800 cm³ - 10 cm³
Volume of the remaining part = 790 cm³
Step 4: Calculate the area of the metal that forms the cuboid.
To calculate the area of the metal that forms the cuboid, we need to know the dimensions of the remaining part. Since the squares were removed from each corner, the length and width of the remaining part will be reduced by twice the length of the side of each square, which is 2 x 5 cm = 10 cm.
Length of the remaining part = 80 cm - 10 cm - 10 cm = 60 cm
Width of the remaining part = 50 cm - 10 cm - 10 cm = 30 cm
Total area of metal that forms the cuboid = 2 × (Length × Height + Width × Height) + Length × Width
Total area of metal that forms the cuboid = 2 × (60 cm × 0.2 cm + 30 cm × 0.2 cm) + 60 cm × 30 cm
Total area of metal that forms the cuboid = 2 × (12 cm² + 6 cm²) + 1800 cm²
Total area of metal that forms the cuboid = 2 × 18 cm² + 1800 cm² = 36 cm² + 1800 cm² = 1836 cm²
So, the area of metal that forms the cuboid is 1836 cm².
b) Calculation of the mass of the empty cuboid:
We know the density of the metal is 2.5 g/cm³, so we can use the formula:
Mass = Volume × Density
To convert the mass to kg, we need to divide the result by 1000.
Mass of the empty cuboid = Volume of the remaining part × Density
Mass of the empty cuboid = 790 cm³ × 2.5 g/cm³
Mass of the empty cuboid = 1975 g = 1.975 kg
So, the mass of the empty cuboid is 1.975 kg.
c) Missing value in the question:
It seems there might be a missing value in your question as you have mentioned a cuboid, but the dimensions of the cuboid are not given. If you provide the dimensions of the cuboid, I can help you calculate the remaining parts.