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6 0

4 years ago

Read 2 more answers

Find the volume of the following solid. Using cylindrical coordinates

Reika [66]

In cylindrical coordinates, the equations of the surfaces become

$z = 4 - 4r^2 \\\\ z = (r^2)^2 - 1 = r^4 - 1$

These surfaces intersect on the cylinder of radius 1 with cross sections parallel to the x,y-plane:

$4 - 4r^2 = r^4 - 1 \\\\ \implies r^4 + 4r^2 - 5 = (r-1)(r+1)(r^2+5) = 0 \\\\ \implies r=1$

Then in cylindrical coordinates, the volume of the space bounded by these surfaces is

$\displaystyle \int_0^{2\pi}\int_0^1\int_{r^4-1}^{4-4r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta = 2\pi \int_0^1 \int_{r^4 - 1}^{4-4r^2}r\,\mathrm dz\,\mathrm dr \\\\ = \pi \int_0^1 (4-4r^2)^2 - (r^4-1)^2 \,\mathrm dr \\\\ = \pi \int_0^1 (15-32r^2+18r^4-r^8)\,\mathrm dr = \boxed{\frac{352\pi}{45}}$

7 0

3 years ago

the cost of a mobile is set Rs.18000.If mrs.Sharma purchased it with 13% VAT. how much did she pay for it.

Klio2033 [76]

Answer:

Rs.20340

Step-by-step explanation:

Cost of the mobile(without VAT) = Rs. 18000

VAT= 13%*18000

=13/100*18000

=13*180

= Rs.2340

Hence, Cost of the mobile phone with VAT= Rs.18000+ Rs. 2340

= Rs.20340

3 0

3 years ago