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Using differentials, estimate the possible error in the volume of a sphere if the radius is measured at 3 0.1± feet.
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- Using differentials, approximate the change, in terms of pi, in the total surface area of a closed right circular cone of radius 3 units and of altitude 5 units if the radius increases by 0.2 unit and the altitude decreases by 0.1 unit.Pls approximate the value using differentialsUse differentials to estimate the amount of material in a closed cylindrical can that is 30 cm high and 12 cm in diameter if the metal in the top and bottom is 0.1 cm thick, and the metal in the sides is 0.05 cm thick. Note, you are approximating the volume of metal which makes up the can (i.e. melt the can into a blob and measure its volume), not the volume it encloses.The differential for the volume (in terms of r,hr,h) isdV=dV= dr+dr+ dhdhThe differentials of rr and hh are:dr=dr= and dh=dh= (be careful)The approximate volume of material is cm3cm3.HINT. The metal fills in the space between two cylinders - the inner one and the outer one. Therefore, the volume of metal equals the increment in the volume VV of the cylinder whose measurements increase from rr and hh to r+drr+dr and h+dhh+dh, respectively. This increment ΔVΔV can be approximated by the differential dVdV.
- Dind differential equatioUse differentials to estimate the amount of tin in a closed tin can with diameter 8 cmand height 12 cm if the tin is 0.04 cm thicWrite the differential formula that estimates the change in the volume look at the picture. Of a sphere when the radius changers from second picture
- A window has the shape of a square surmounted by semi-circle. The base of the window has a width of 60 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum error possible in computing the area of the window.Use differential to approximate the change in the volume of a sphere when its radius changes from 2 to 2.1. The volume of a sphere of radius r is 4/3pir^3The radius of a circular disk is given by 18cm. with maximum error in measurement of 0.1cm. Use differential to calculate the maximum error in calculated area of the disk. What is the error relative to the area?
- Use differentials to estimate (or approximate) the amount of tin in a closed tin box with height 6cm, width 11cm, and length 10cm, if the tin is 0.03 cm thick. Include units.Use differentials to estimate the amount of paint needed to apply a cost of paint 0.06 cm thick to a hemispherical dome with diameter 54 m. (Round your answer to two decimal places.)Use differentials to estimate the amount of metal in a closed cylindrical tin can with diameter 8 cm and height 12 cm if the metal on the top and the bottom is 0.2 cm thick and the metal on the sides is 0.1 cm thick.