Question

A solid cuboidal slab of iron of dimensions 77 cm × 10 cm × 17 cm is used to cast an iron pipe. If the outer diameter of the pipe is 5 cm and thickness is 0.5 cm.Then calculate the length of the pipe.

Answer 1

Answer:

The length of pipe is 1851.1 (approx.)

Step-by-step explanation:

Given: Dimension of cuboidal slab of iron are 77 cm × 10 cm × 17 cm

           Outer Diameter of pipe = 5 cm & thickness of pipe = 0.5 cm

To find : Length of pipe

let the length of pipe be l.

Inner diameter of pipe = 5 - ( 0.5 + 0.5 ) = 4 cm

⇒Inner radius of pipe, $r_1$ = $\frac{4}{2}$ = 2 cm

⇒Outer radius of pipe, $r_2$ = $\frac{5}{2}$ = 2.5 cm

According to question,

volume of pipe = volume of Slab of iron

$\pi (r_2)^2h - \pi (r_1)^2h = l\times b\times h\\\pi h [(r_2)^2 - (r_1)^2] = l\times b \times h\\\\\frac{22}{7}\times l\times[2.5^2-2^2]=77\times10\times17\\\\\frac{22}{7}\times 2.25\times l=13090\\\\\frac{49.5}{7}\times l =13090\\\\l=\frac{13090\times7}{49.5}\\\\l=1851.1 \:(approx.)$

Therefore, The length of pipe is 1851.1 (approx.)

Answer 2

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Dimensions of cuboidal slab = 77cm * 10cm * 17cm

Outer radius of pipe ,R = 5cm

Inner radius of pipe ,r = outer radius - thickness = 5 - 1 = 4cm

Volume of cuboidal slab = volume of pipe

l * b * h = pi*R*R*h - pi*r*r*h

l * b * h = pi*h (R*R -r*r)

77*10*17 = 22/7 * h (5*5 - 4*4)

77 * 17 * 10 * 7/22 = h (25-16)

84.14 is correct answer

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