a closed box of uniform thickness is made of wood 1cm thick. Its extenal dimensions are 6cm and 5 cm by 4 cm. Find the
a. volume of the wood used in making the box.
b. the capacity of the box, given that the cover is full length and full width
c. The interior surface area if the box is left open
I assume the height of 4 cm includes the cover
outside box is 6 x 5 x 4
inside it is 4 x 3 x 2
volume outside = 120
volume inside = 24 (b)
so volume wood = 120 - 24 = 96 (a)
length = 4
width = 3
depth = 2 -1 for cover = 1
so area bottom inside = 4*3 = 12
area sides = 2*4*1 = 8
area ends = 2 *3 * 1 = 6
so
12 + 8 + 6 = 26
To find the volume of the wood used in making the box, we need to find the difference between the volume of the box and the volume of the empty space inside.
a. Volume of the box:
The external dimensions of the box are given as 6 cm, 5 cm, and 4 cm. To find the volume, we multiply these dimensions together:
Volume of the box = 6 cm * 5 cm * 4 cm = 120 cm^3
b. Volume of the empty space:
The internal dimensions of the box are calculated by subtracting twice the thickness of the wood from the external dimensions:
Internal dimensions = (6 cm - 2 * 1 cm) * (5 cm - 2 * 1 cm) * (4 cm - 2 * 1 cm)
= 4 cm * 3 cm * 2 cm
= 24 cm^3
c. Volume of the wood used:
Volume of the wood used = Volume of the box - Volume of the empty space
= 120 cm^3 - 24 cm^3
= 96 cm^3
Therefore, the volume of the wood used in making the box is 96 cm^3.
To find the capacity of the box, given that the cover is full length and full width, we simply calculate the volume of the empty space inside the box.
b. Capacity of the box:
Capacity of the box = Volume of the empty space
= 24 cm^3
Therefore, the capacity of the box is 24 cm^3.
To find the interior surface area of the box if it is left open, we need to calculate the surface area of each face excluding the face which is closed by the cover.
c. Interior Surface Area of the box:
The box has 6 faces. One face is covered, so we will calculate the surface area of the remaining 5 faces.
Surface area of one face = length * width
= (5 cm - 2 * 1 cm) * (4 cm - 2 * 1 cm)
= 3 cm * 2 cm
= 6 cm^2
Therefore, the interior surface area of the box is 5 * 6 cm^2 = 30 cm^2.