SURFACE AREAS
AND VOLUMES
l
3.5 cm
Q. A toy is in the form of a cone of radius 3.5 cm mounted on a
hemisphere of same radius. The total height of the toy is 15.5 cm.
Find the total surface area of the toy.
15.5cm
Total surface area of toy =
CSA of cone (S1) +
CSA of hemisphere (S2)
The entire toy is made up of a cone and a hemisphere
3.5 cm
?
Height of cone
= Height of vessel
– Height of Hemisphere
15.5 –
=
3.5
12 cm
=
Sol.
12 cm
We know that,
Radius =
Height
In Hemisphere,
Let us find the slant height (l )
π r l
2 π r2
✔
?
✔
What is the formula to find curved surface area of cone ?
What is the formula to find curved surface area of the hemisphere?
What is the formula to find slant height (l )?
For getting the slant height (l ),
Let us first find height (h)
Sol.
Slant height (l )
=
r2
+
h2
=
(3.5)2
+
122
=
12.25
+
144
15.5cm
3.5cm
=
156.25
=
12.5 cm
Surface area of cone (S1)
=
π r l
=
π
× 3.5
× 12.5
=
43.75πcm2
3.5cm
12cm
∴
l
Surface area of cone (S1)
∴
12.5 cm
l
Q. A toy is in the form of a cone of radius 3.5 cm mounted on a
hemisphere of same radius. The total height of the toy is 15.5 cm.
Find the total surface area of the toy.
Total surface area of toy =
CSA of cone (S1) +
π r l
2 π r2
CSA of hemisphere (S2)
✔
?
✔
✔
Sol.
Surface area of hemisphere(S2)
=
2πr2
=
2π
× (3.5)2
=
24.5πcm2
Total surface
area of the toy
=
S1 + S2
=
43.75π
+
24.5π
=
68.25π
=
68.25
7
×
22
=
214.25 cm2
9.75
15.5cm
3.5cm
12cm
Total surface area of the toy is 214.25 cm2.
3.5cm
S1 = 43.75π
∴
Surface area of hemisphere(S2)
∴
Q. A toy is in the form of a cone of radius 3.5 cm mounted on a
hemisphere of same radius. The total height of the toy is 15.5 cm.
Find the total surface area of the toy.
Total surface area of toy =
CSA of cone (S1) +
π r l
2 π r2
CSA of hemisphere (S2)
=
2π
× 3.5
× 3.5