A play-topis in the form of a hemisphere surmounted
on avcone.The diameter of the hemisphere is 3.6cm.
The total height of the play-topis 4.2cm.Find its
total surface area.
Answers
Answer:
.Let r and h are radius and height of the cone.
diameter of the hemisphere = 3.6 cm
radius of hemisphere (r) = (3.6)/2 = 1.8 cm
total height of the play top = 4.2cm
radius of hemisphere + height of cone = 4.2
1.8 + h = 4.2
h = 4.2 - 1.8
h = 2.4 cm
Now we are going to find slant height of cone
L² = r² + h²
= (1.8)² + (2.4)²
= 3.24 + 5.76
L² = 9
L = √3 x 3
L = 3 cm
To find the total surface area of the play top we have to find the sum of curved surface area of hemisphere and curved surface area of cone.
Total surface area of play top = C.S.A of hemisphere + C.S.A of cone
= 2 Π r² + Π r L
= Π r [2 r + L]
= Π x (1.8) [2(1.8) + 3]
= Π x (1.8) [3.6 + 3]
= Π x (1.8) [6.6]
= 11.88 Π cm²
Total surface area of the play top = 11.88 Π cm²
Answer:
