# A toy in the shape of solid cylinder surmounted by a conical top.If the height of the diameter of the cylinder path are 21cm and 40cm respectively and height of the cone is 15cm.Find the total surface area of the toy. use pie=3.14

Let r and h be the radius and height of the cylindrical part.

Suppose R and H be the radius and height of the conical top. R = 20 cm and H = 15 cm

Slant height of the cone, Total surface of the toy

= Curved surface area of cone + Curved surface area of cylinder + Area of base

= πRl + 2πrh + πr2

= π(20 × 25 + 2 × 20 × 21 + 20 × 20) cm2

= 3.14 × (500 + 840 + 400) cm2

= 3.14 × 1740 cm2

= 5463.6 cm2

Thus, the total surface area of the toy is 5463.6 cm2.

• 6

let the hieght of cylinder be H and radius be R

and let the hieght of cone be h and radius will be same as that of cylinder as it is surmounted on cylinder.

given H=21 cm

R=40/2=20cm

h=15cm

TSA=csa of cone +csa of cylinder+area of circular base

= 3.14 * r * l(slant hieght) + 2 * 3.14 * R * H + 3.14 * R2 * H  --(1)

l2 =h2+r2

=(15)2+(20)2

=225+400

=625

l=25cm

putting this in equation 1

3.14 * 20 * 25 + 2 * 3.14 * 20 * 21 + 3.14 * 20 * 20

=3.14 * 20  [ 25 + 2 * 21 + 20]

=62.8  [25 + 42 + 20]

=62.8 * 87

=5463.6cm2

• 4

we have

diameter of cylinder=40 cm

radius of cylinder is (r)=40/2= 20 cm

heigth of cylinder(h)=21 cm

& radius of cone (R) =20 cm , height of cone (H)=15 cm

slant height (l)=H2+R2

l2=152+202 =225+400 =625

l=25 cm

total surface area of toy=c.s.a  of cylinder+ c.s.a of cone +ar.of base of cylinder

=2*3.14*r*h + 3.14*R*l + 3.14*r2

=3.14(2*20*21 +15*25 +202)  = 3.14 (840+375 +400)

= 3.14*1615 = 5071.1 cm2

therefore, t.s.a of toy is 5071.1 cm2

• 0
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