SURFACE AREAS
AND VOLUMES
8 cm
8.5 cm
Volume of glass vessel =
Vol. of cylinder (V1) +
What is the formula to find volume of sphere?
What is the formula to find volume of cylinder?
Vol. of sphere (V2)
Sol.
Radius of cylinder (r1)
=
1 cm
2
2
=
Radius of sphere (r2)
=
8.5
2
To check whether the child is correct, let us calculate volume of the glass vessel.
2 cm
Q. A spherical glass vessel has a cylindrical neck 8 cm long,
2 cm in diameter; the diameter of the spherical part is 8.5 cm.
By measuring the amount of water it holds, a child finds its volume
to be 345 cm3. Check whether she is correct, taking the above as the
inside measurements. (π = 3.14)
π r12 h
?
✔
✔
πr23
×
4
3
?
✔
Volume of glass vessel =
Vol. of cylinder (V1) +
Vol. of sphere (V2)
Q. A spherical glass vessel has a cylindrical neck 8 cm long,
2 cm in diameter; the diameter of the spherical part is 8.5 cm.
By measuring the amount of water it holds, a child finds its volume
to be 345 cm3. Check whether she is correct, taking the above as the
inside measurements. (π = 3.14)
π r12 h
Sol.
Radius of cylinder (r1)
=
1 cm
2
2
=
=
π
×
(1)2
×
8
=
8 π cm3
Vol. of cylinder (V1)
=
πr12h
∴
Vol. of cylinder (V1)
πr23
×
4
3
Radius of sphere (r2)
=
8.5
2
=
π
×
Vol. of sphere (V2)
×
4
3
8.5
2
=
πr23
Vol. of sphere (V2)
×
×
8.5
2
×
8.5
2
4
3
8 cm
2 cm
8.5 cm
Volume of glass vessel =
Vol. of cylinder (V1) +
Vol. of sphere (V2)
=
π
×
Vol. of sphere (V2)
×
=
π
×
×
=
× π
=
102.354π cm3
4
3
4
3
614125
6 × 1000
8.5
2
Q. A spherical glass vessel has a cylindrical neck 8 cm long,
2 cm in diameter; the diameter of the spherical part is 8.5 cm.
By measuring the amount of water it holds, a child finds its volume
to be 345 cm3. Check whether she is correct, taking the above as the
inside measurements. (π = 3.14)
π r2 h
Sol.
85
20
×
85
20
×
85
20
2
10
10
π × 85 × 85 × 85
6
=
×
1000
=
102354.16
1000
Vol. of sphere (V2)
∴
πr3
×
4
3
×
8.5
2
×
8.5
2
π
8 cm
2 cm
8.5 cm
Q. A spherical glass vessel has a cylindrical neck 8 cm long,
2 cm in diameter; the diameter of the spherical part is 8.5 cm.
By measuring the amount of water it holds, a child finds its volume
to be 345 cm3. Check whether she is correct, taking the above as the
inside measurements. (π = 3.14)
Sol.
Vol. of glass vessel
=
V1
=
8 π
+
102.354 π
=
110.354 π cm3
+
V2
=
110.354
×
3.14
=
346.51 cm3
The volume found by the child, i.e., 345 cm3 is incorrect.
V2 =102.354π
∴
Volume of glass vessel =
Vol. of cylinder (V1) +
Vol. of sphere (V2)
∴ Vol. of glass vessel
A child finds the volume to be 345 cm3
8 cm
2 cm
8.5 cm