A CYLINDRICAL PIPE MADE OF METAL IS 3 CM THICK .IF THE INTERNAL RADIUS OF THE PIPE IS 10 CM, FIND THE VOLUME OF THE METAL USED IN MAKING 3M OF THE PIPE
RADIUS OF INTERNAL PIPE =10CM RADIUS OF EXTERNAL PIPE =13CMVOLUME OF PIPE=PI R^2H
20700
how did they get 20700
A cylindrical pipe made of metal is 3cm thick.if the internal radius of the pipe is 10cm find the volume of the metal used in making 3cm of the pipe
The external (outer) radius of the pipe can be found by adding the thickness to the internal radius:
External radius = internal radius + thickness = 10cm + 3cm = 13cm
The length of the pipe is given as 3m = 300cm.
Using the formula for the volume of a cylinder (V = πr^2h), we can find the volume of the metal used by subtracting the volume of the internal cylinder from the volume of the external cylinder:
Volume of external cylinder = π(13cm)^2(300cm) = 153,938.04 cm^3
Volume of internal cylinder = π(10cm)^2(300cm) = 94,247.78 cm^3
Volume of metal used = Volume of external cylinder - Volume of internal cylinder
Volume of metal used = 153,938.04 cm^3 - 94,247.78 cm^3
Volume of metal used = 59,690.26 cm^3
Therefore, the volume of metal used in making 3m of the pipe is approximately 59,690.26 cubic cm.
To calculate the volume of the wood, we need to find the external dimensions of the box. Since the box is open, the thickness of the wood will only affect two dimensions (length and width) and we can ignore it for the depth (height) dimension.
External length = Internal length + 2 × Wood thickness = 2 cm + 2 × 2.5 cm = 7 cm
External width = Internal width + 2 × Wood thickness = 20 cm + 2 × 2.5 cm = 25 cm
External height (depth) = Internal height + Wood thickness = 22.5 cm + 2.5 cm = 25 cm
Now we can calculate the volume of the wood by subtracting the volume of the internal box from the volume of the external box.
Volume of internal box = Internal length × Internal width × Internal height = 2 cm × 20 cm × 22.5 cm = 900 cubic cm
Volume of external box = External length × External width × External height = 7 cm × 25 cm × 25 cm = 4375 cubic cm
Volume of wood = Volume of external box - Volume of internal box
Volume of wood = 4375 cubic cm - 900 cubic cm
Volume of wood = 3475 cubic cm
Therefore, the volume of wood used in making the box is 3475 cubic cm.