Math
A carpenter constructed a closed wooden box with internal measurements 1.5m long 0.8m width and 1m high. wood used in constructing the box was 1cm thick and density of 0.6g/cm. Find volume of the wood used in constructing the box
2.mass of the box in kg correct to 1decimal place
I want an answer
To find the volume of the wood used in constructing the box, we need to calculate the difference between the outer and inner volumes.
1. Calculate the outer volume of the box:
Outer Volume = Length x Width x Height
= 1.5m x 0.8m x 1m
= 1.2 m³
2. Calculate the inner volume of the box:
Inner Volume = (Length - 2 x Thickness) x (Width - 2 x Thickness) x (Height - 2 x Thickness)
= (1.5m - 2 x 0.01m) x (0.8m - 2 x 0.01m) x (1m - 2 x 0.01m)
= (1.48m) x (0.78m) x (0.98m)
= 1.1376 m³
3. Calculate the volume of the wood used:
Volume of Wood = Outer Volume - Inner Volume
= 1.2 m³ - 1.1376 m³
= 0.0624 m³
Therefore, the volume of the wood used in constructing the box is 0.0624 cubic meters.
To find the mass of the box, we'll multiply the volume of the wood by its density.
4. Calculate the mass of the box:
Mass of the Box = Volume of Wood x Density
= 0.0624 m³ x 0.6 g/cm³
= 0.03744 g
≈ 0.0374 kg (rounded to 1 decimal place)
Therefore, the mass of the box is approximately 0.0374 kg.
To find the volume of the wood used in constructing the box, we first need to calculate the volume of the outer box and the volume of the inner box. Then, we subtract the volume of the inner box from the volume of the outer box to get the volume of the wood.
1. Calculate the volume of the outer box:
The internal measurements given are 1.5m (length) x 0.8m (width) x 1m (height). To find the volume, we need to take into account the thickness of the wood. Since the wood is 1cm thick on all sides, we add 2cm to each dimension to get the dimensions of the outer box. Therefore, the dimensions of the outer box are 1.5m + 2cm (thickness) x 0.8m + 2cm (thickness) x 1m + 2cm (thickness).
Converting the thickness to meters, we have 1.5m + 0.02m x 0.8m + 0.02m x 1m + 0.02m.
Calculating this, we have 1.52m x 0.82m x 1.02m.
2. Calculate the volume of the inner box:
The given internal measurements are 1.5m (length) x 0.8m (width) x 1m (height).
3. Calculate the volume of the wood used:
Now we subtract the volume of the inner box from the volume of the outer box to get the volume of the wood used.
Volume of wood used = Volume of outer box - Volume of inner box.
To calculate the mass of the box, we need to multiply the volume of the wood used by the density of wood.
The density of wood is given as 0.6g/cm³. We will convert the volume of the wood from cubic meters to cubic centimeters and then multiply by the density to get the mass in grams. Finally, we convert the mass to kilograms and round it to one decimal place.
Note: 1 cubic meter = 1,000,000 cubic centimeters (cm³).
Now we can proceed with the calculations:
1. Calculate the volume of the wood used:
Volume of outer box = 1.52m x 0.82m x 1.02m = 1.26096 m³.
Volume of inner box = 1.5m x 0.8m x 1m = 1.2 m³.
Volume of wood used = 1.26096 m³ - 1.2 m³ = 0.06096 m³.
2. Calculate the mass of the wood used:
Volume of wood used = 0.06096 m³ = 0.06096 x 1,000,000 cm³ = 60,960 cm³.
Mass of the wood used = Volume of wood used x Density of wood = 60,960 cm³ x 0.6 g/cm³ = 36,576 g.
Converting the mass to kilograms and rounding it to one decimal place:
Mass of the box = 36,576 g = 36.6 kg (rounded to 1 decimal place).
Therefore, the volume of wood used in constructing the box is 0.06096 cubic meters, and the mass of the box is 36.6 kg (correct to 1 decimal place).
L = Length
L = 1.5 m = 150 cm
W = Width
W = 0.8 m = 80 cm
H = Height
H = 1 m = 100 cm
Volume of the outside side of the box:
Vo = L ∙ W ∙ H = 150 ∙ 80 ∙ 100 = 1 200 000 cm³
The dimensions of the inner side are less than 1 cm thick on the right side and 1 cm thick on the left side.
So the internal dimensions are less than the external dimensions by 2 cm.
Volume of the internal side of the box:
Vi = ( L - 2 ) ∙ ( W - 2 ) ∙ ( H - 2 ) = 148 ∙ 78 ∙ 98 = 1 131 312 cm³
Volume of the wood = Volume of the outside side of the box - Volume of the internal side of the box
Ww= Vo - Vi = 1 200 000 - 1 131 312 = 68 688 cm³
1 kg = 1000 g
1 g = 1 kg / 1000
Density:
ρ = 0.6 g / cm³
ρ = ( 0.6 g / cm³ ) / 1000
ρ = 0.0006 kg / cm³
Mass of the box = Density ∙ Volume of the wood
m = 0.0006 kg / cm³ ∙ 68 688 cm³ = 28.0704 kg
m = 28.1 kg
to one decimal place
Remark:
28.0704 kg is 0.0704 kg away from 28 kg and 0.0296 kg from away 28.1 kg.
So 28.0704 kg is closer to 28.1 kg than 28 kg