SURFACE AREAS
AND VOLUMES
Sol.
r =
1.4
2
= 0.7 cm
What is the formula to find curved surface area of cylinder?
What is the formula to find area of a circle?
TSA (remaining solid) =
What is the formula to find curved surface area of cone?
Diameter =
1.4 cm
d
2
=
∴
Slant height (l )
=
r2
+
h2
=
(0.7)2
+
(2.4)2
=
0.49
+
5.76
=
6.25
=
2.5 cm
∴
l
What is the shape of the
base of the cylinder ?
Circle
Area of base +
CSA of cylinder (S1) +
CSA of cone (S2)
0.7
625
100
=
25
10
=
What is the formula to find slant height (l )?
l
=
r2
+
h2
2.4cm
1.4cm
Q. From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm,
a conical cavity of the same height and same diameter is hollowed out.
Find the total surface area of the remaining solid to the nearest cm2.
π r l
?
?
2 π r h
✔
?
✔
π r2
?
✔
✔
✔
Q. From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm,
a conical cavity of the same height and same diameter is hollowed out.
Find the total surface area of the remaining solid to the nearest cm2.
TSA (remaining solid) =
Area of base +
CSA of cylinder (S1) +
CSA of cone (S2)
Sol.
π r l
CSA of cone (S2)
= π ×
= 1.75π cm²
h = 2.4 cm,
r = 0.7 cm,
0.7
× 2.5
Area of the base of cylinder
= πr2
= π
×
(0.7)2
= 0.49π cm2
CSA of cyl. (S1)
= 2πrh
=
2
×
π
×
0.7
=
3.36π cm2
×
2.4
=
l = 2.5 cm
π r l
2 π r h
π r2
=
0.14
×
π
×
2.4
∴ CSA of cyl. (S1)
∴ CSA of cone (S2)
2.4cm
1.4cm
Q. From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm,
a conical cavity of the same height and same diameter is hollowed out.
Find the total surface area of the remaining solid to the nearest cm2.
TSA of the remaining solid
=
=
= 5.6π
= 5.6 ×
S1
+ S2
Area of the base +
+ 3.36π
+ 1.75π
0.49π
22
7
=
0.8
×
22
=
17.6 cm²
TSA of the remaining solid is 18 cm2
S1 = 3.36π
S2 = 1.75π
Area of base = 0.49π
∴
0.8
π r l
2 π r h
π r2
Sol.
TSA (remaining solid) =
Area of base +
CSA of cylinder (S1) +
CSA of cone (S2)
2.4cm
1.4cm