the metal with the volume of 1496 cm cube is used to cast a pipe of length 28 CM if the internal radius of the pipe is 8 cm find its outer radius
Answers
If the internal radius of the pipe is 8 cm and length is 28 cm, then its outer radius is 9 cm.
Step-by-step explanation:
The volume of the metal = 1496 cm³
The length of the pipe i.e., its height = 28 cm
The Inner radius, r = 8 cm
Let the outer radius of the pipe be denoted as “R”.
Since the metal is cast into a hollow pipe, so the volume of the metal will be equal to the volume of the hollow pipe.
Therefore,
The volume of the hollow pipe = π*h [R² – r²]
⇒ 1496 = (22/7) * 28 * [R² – 8²]
⇒ [R² - 64] = 1496/[22*2]
⇒ R² = 17 + 64
⇒ R² = 81
⇒ R = 9 cm
Thus, the outer radius of the pipe is 9 cm.
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- length =28
radius 1=8cm
Therefore,
Volume of hollow cylinder=pie× height (R+r) (R-r)
1496 =22/7×28(8+r) (8-r) =88×64+r^2
1496÷88=r^2+64
r^2=64+17
r^2=81
r=√9×9
r=9