The radius of the base of a cylindrical wooden block is 6 cm and its volume is 1320 cu. cm. How many discs of radius 5 cm and height 2 cm can be cut from this block of wood?
The volume of the cylindrical wooden block can be calculated as:
V = πr²h
[tex]{\rule{200pt}{5pt}}[/tex]
Where,
r is the radius of the base of the cylinder and h is its height.
[tex]{\rule{200pt}{5pt}}[/tex]
Substituting the given values, we get:
1320 = π6²h
h = 11.55 cm (approx.)
[tex]{\rule{200pt}{5pt}}[/tex]
Now, each disc that is cut from the block has a volume of:
Vd = πr²h
= π(5²)(2)
= 50π cu. cm
[tex]{\rule{200pt}{5pt}}[/tex]
The maximum number of such discs that can be cut from the cylindrical block is given by the ratio of the volume of the block to the volume of each disc:
n = V/Vd
= 1320/(50π)
≈ 8.4
[tex]{\rule{200pt}{5pt}}[/tex]
Therefore,
A maximum of 8 discs of radius 5 cm and height 2 cm can be cut from this block of wood.
[tex]{\rule{200pt}{5pt}}[/tex]
[tex]\sf{ \color{pink}{⊱☆゚Hope \: this \: helps \: uh \: !!}}[/tex]
The radius of the base of a cylindrical wooden block is 6 cm and its volume is 1320 cu. cm. How many discs of radius 5 cm and height 2 cm can be cut from this block of wood
Answers & Comments
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge\underline{\overline{\mid{\bold{\red{{Answer}}\mid}}}}[/tex]
[tex]{\rule{200pt}{5pt}}[/tex]
The volume of the cylindrical wooden block can be calculated as:
[tex]{\rule{200pt}{5pt}}[/tex]
Where,
[tex]{\rule{200pt}{5pt}}[/tex]
Substituting the given values, we get:
[tex]{\rule{200pt}{5pt}}[/tex]
Now, each disc that is cut from the block has a volume of:
[tex]{\rule{200pt}{5pt}}[/tex]
The maximum number of such discs that can be cut from the cylindrical block is given by the ratio of the volume of the block to the volume of each disc:
[tex]{\rule{200pt}{5pt}}[/tex]
Therefore,
[tex]{\rule{200pt}{5pt}}[/tex]
[tex]\sf{ \color{pink}{⊱☆゚Hope \: this \: helps \: uh \: !!}}[/tex]
The radius of the base of a cylindrical wooden block is 6 cm and its volume is 1320 cu. cm. How many discs of radius 5 cm and height 2 cm can be cut from this block of wood