Appropriate Question:
The metal with the volume of 1496[tex]\sf\:cm^3 [/tex] is used to cast a pipe of length 28 cm. If internal radius of the pipe is 8 cm, find its outer radius.
Answer:
Outer radius of a pipe is 9 cm
Step-by-step explanation:
Let assume that r, h and R represents the inner radius, length and outer radius of a pipe respectively.
So, We have given that
Inner radius of pipe, r = 8 cm
Length of pipe, h = 28 cm
Further given that, Volume of metal used = [tex]\sf\:1496\: cm^3 [/tex]
[tex]\sf\: \pi( {R}^{2} - {r}^{2} )h = 1496 \\ [/tex]
[tex]\sf\: \dfrac{22}{7} \times ( {R}^{2} - {8}^{2} ) \times 28 = 1496 \\ [/tex]
[tex]\sf\:22 \times ( {R}^{2} - 64 ) \times 4 = 1496 \\ [/tex]
[tex]\sf\:22 \times ( {R}^{2} - 64 ) = 374 \\ [/tex]
[tex]\sf\: {R}^{2} - 64 = 17 \\ [/tex]
[tex]\sf\: {R}^{2} = 64 + 17 \\ [/tex]
[tex]\sf\: {R}^{2} = 81 \\ [/tex]
[tex]\implies\sf\:R = 9 \: cm \\ [/tex]
Hence, outer radius of a pipe is 9 cm.
