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3 years ago

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A rectangular plate casting has dimensions 200mm x 100mm x 20mm. The riser for this sand casting mold is in the shape of a spher

e. The casting takes 3.5mins to solidify. Calculate the diameter of the riser so that it takes 20% longer for the riser to solidify

1 answer:

9966 [12]3 years ago

3 0

Answer:

Diameter of riser =6.02 mm

Explanation:

Given that

Dimensions of rectangular plate is 200mm x 100mm x 20mm.

Volume of rectangle V= 200 x 100 x 20 $mm^3$

Surface area of rectangle A

A=2(200 x 100+100 x 20 +20 x 200) $mm^2$

So V/A=7.69

We know that

Solidification times given as

$t=K\left(\dfrac{V}{A}\right)^2$ -----1

Lets take diameter of riser is d

Given that riser is in spherical shape so V/A=d/6

And

Time for solidification of rectangle is 3.5 min then time for solidificartion of riser is 4.2 min.

Lets take $\dfrac{V}{A}=M$

$\dfrac{M_{rac}}{M_{riser}}=\dfrac{7.69}{\dfrac{d}{6}}$

Now from equation 1

$\dfrac{3.5}{4.2}=\left(\dfrac{7.69}{\dfrac{d}{6}}\right)^2$

So by solving this d=6.02 mm

So the diameter of riser is 6.02 mm.

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Answer:

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Explanation:

Solution:-

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- We are to test the claim made by the civil engineer regarding the mean compressive strength of the concrete. The data of compressive strength of each specimen from the sample is given below:

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- The rejection region for the hypothesis is defined by the significance level ( α = 0.01 ). The Z-critical value ( limiting value for the rejection region ) is determined:

Z-critical = Z_α/2 = Z_0.005

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Z-critical = Z_0.005 = ± 2.576

- Compare the Z-test value against the rejection region defined by the Z-critical value.

Rejection region: Z > 2.576 or Z < -2.576

- The Z-test value lies in the rejection region:

Z-test < Z-critical

-27.24 < -2.576 .... Null hypothesis rejected

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[ 3251.33 - 2.58*√(1000 / 12) < μ < 3251.33 + 2.58*√(1000 / 12) ]

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