Question

A company produces a spherical object of radius 26 centimeters. A hole of radius 4 centimeters is drilled through the center of the object.

(a) the volume of the object

(b) the outer surface area of the object

A company produces a spherical object of radius 26 centimeters. A hole of radius 4 centimeters is drilled through the center of the object. (a) the volume of the object 1760V 165 T cm3 (b) the outer surface area of the object 22561 cm2

Answer 1

Sor o we have Asos 26 and os os at z² = 26-x² - y²z =526²x²_42 Integral set, we will say and osos / multiply by 8 to accounts for all of the semi- hemisphere. 1/2 26 V = du= - 28d8 Let u= 26²_82 het u= 26*-*? V285 352.61-3 vir die Ydy do 2-72 12 TY2 =-41$. (622-25).* 40 SC6603" do 3 48.607 - 7 1760 5165 ) comment 6 Z = 5262-82_y2 -y dA surface Area = SS Sit zu + 2;} dA Surface Areas <x Convert to polar form than,x=rcoso, sarsino and x²+ y² =22 dA=&drdo

Surface Area = or 2 26 sufrece areas and is it riento pronto par de a +- 82cos²o ² sinto drde t 2,2 26² zz 1/2 26 + 72 26²-22 z dr de 1262 J 26²-82 : 4 using substitution , u= 26-82 du = -27 de - 1/2 E12 26 26 T\/2 Dans le acusay" so 5-8 may ganito -0620) 5 - so do * 4x208 Stas.so] 24208. stor. 5 [pos svas tj cm2 the object the outer surface Area of Therefore [208 5765 to] em?