A toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of the conical portion is 6 cm and its height is 4 cm. Determine the surface area of the toy. (Use π = 3.14)
Answers
Answer:
The curved surface area of the toy is 103.62 cm² .
Step-by-step explanation:
SOLUTION :
Given :
Height of the cone (h) = 4cm
Diameter of the cone (d) = 6 cm
Radius of the cone & hemisphere , (r) = 3 [
Let, ‘l’ be the slant height of cone.
l = √r² + h²
l = √3² + 4² = √9 + 16 = √25
l = √25
l = 5 cm
Slant height of the cone (l) = 5 cm
Curved surface area of the cone (S1) = πrl
S1 = π(3)(5) = 15π cm²
S1 = 15π cm²
Curved surface area of the hemisphere (S2) = 2πr²
S2 = 2π(3)² = 2π × 9 = 18π cm²
S2 = 18π cm²
Total surface area of toy (S) = S1 + S2
S = 15π + 18π = π(15 + 18)
S = 3.14 × 33
[Given : π = 3.14 ]
S = 103.62 cm²
Hence, the curved surface area of the toy is 103.62 cm² .
HOPE THIS ANSWER WILL HELP YOU….
Conical portion
r=3cm,h=4cm
l
2
=r
2
+h
2
=3
2
+4
2
=9+16
l
2
=25
l=
25
=5cm
Spherical portion r=3cm
Surface area of the toy= CSA of hemisphere+ CSA of cone
=2πr
2
+πrl=2×
7
22
×3×3cm
2
+
7
22
×3×5cm
2
=
7
396
cm
2
+
7
330
cm
2
=
7
726
cm
2
=103.71cm
2
Surface area of the toy=103.71cm
2
Volume of the toy= Volume of hemisphere+ Volume of cone
=
3
2
πr
3
+
3
1
πr
2
h=
3
2
×
7
22
×3×3×3cm
3
+
3
1
×
7
22
×3×3×4cm
3
=
7
396
cm
3
+
7
264
cm
3
=
7
660
cm
3
∴ Volume of the toy=94.28cm
3