Hiya, anyone any good at area and volume??!
Question: Please I need your help with this question thanks :)
From a rectangle block 14cm long, 7cm wide and 3cm thick, three cylindrical holes are drilled of equal size. If the volume of the block is reduced by one third, calculate the diameter of each hole in centimeters to the nearest cm.
Answers: Please I need your help with this question thanks :)
From a rectangle block 14cm long, 7cm wide and 3cm thick, three cylindrical holes are drilled of equal size. If the volume of the block is reduced by one third, calculate the diameter of each hole in centimeters to the nearest cm.
Let V be the volume of the block
V = 14 x 7 x 3
The volume of the holes is 1/3 of that,so
Vholes= 7x14 x 3/x = 7x 14 =98
Vholes = 3 Vhole
Vhole = Pi R^2 x depth
so 3xPiR^2 x depth = 98
Note that the question does not tell us which side the holes are drilled in so the depth can only be 3, 7 or 14
try depth = 3
3 Pi R^2 x 3 = 98
R = sqrt(98/3/3/3.14159) R = 1.86cm
So the diameter is 3.72 and the holes could then fit in the 14 cm long face of the block
if the depth is 7
Then
R = sqrt(98/3/7/3.14159) R = 1.22 cm
Then the diameter is 2.4 , this again will fit in the 14 cm side
You can try the 14cm depth and see what you get.
Hope this helps
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Okay, so the beginning volume of that is 294 cm I think because it's 14 x 7 x 3.. One third of that is 98 cm. Then divide that by 3 since there are three cylindrical holes. Which is 32.666667 cm. That's as far as I can get. Sorry.
It will depend on which side they drill the hole
1.21 cm if on the 7 cm side
1.86 cm if on the 3 cm side
0.86 if on the 14 cm side
This would assume that they would drill the hole all the way through.