2.) Five star pizza claims that their pizzas are circular with a diameter of 50
ID: 2850261 • Letter: 2
Question
2.) Five star pizza claims that their pizzas are circular with a diameter of 50 cm. estimate the quantity of pizza lost or gained if the diameter is off by at most 1.2cm.
3.) the radius of a sphere was measured and found to be 21 cm with a possible error in measurement of at most 0.05cm. what is the maximum error in using this value of the radius to compute the surface area of the sphere?
4.) the radius of a sphere ball is measured at r=15cm. If the ball is to be painted, covering the ball in 0.3 cm of paint, use differentials to estimate the amount of paint used on the ball.
5.) the dosage D of diphenhydramine for dog of body mass w kg is D=4.7w^(2/3) mg. estimate the maximum allowable error in w for a dog of mass w=10kg if the percentage error in D must be less than 3%
Explanation / Answer
2.) Five star pizza claims that their pizzas are circular with a diameter of 50 cm. estimate the quantity of pizza lost or gained if the diameter is off by at most 1.2cm.
area of pizza A=pi r2 where r is radius.
diameter d=2r ==>r =d/2
A=pi (d/2)2
A=(pi/4)d2
diameter d=50cm,diameter is off by at most 1.2cm==>dd=-1.2cm
quantity of pizza lost or gained =dA=(pi/4)2*d* dd
dA=(pi/2)*50* (-1.2)
dA=-30pi
94.25cm2
quantity of pizza lost =30pi=94.25cm2
3)surface area os sphere s=4 pi r2
where r is radius
ds=4 pi *2r *dr
r=21cm,dr=0.05cm
ds=4 pi *2*21 *0.05
ds=8.4pi cm2
ds=26.4cm2
maximum error in using this value of the radius to compute the surface area of the sphere=26.4cm2
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