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I need help with this Mathematics question

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Forgotten the formula for volume of a cone. Treat each end as a cone and the middle as a cylinder.

To find the volume of the pencil, which consists of a central cylinder and two cones (one at each end), we use the following data from your diagram:

Length of the cylindrical part: 16 cm

Radius of the pencil: 1 cm

Length of each cone: 1.2 cm

Use
π
=
22
7
π=
7
22


Step 1: Volume of the Cylinder

Volume
cylinder
=
π
r
2
h
=
22
7
×
(
1
)
2
×
16
=
22
7
×
16
=
50.29

cm
3
Volume
cylinder
=πr
2
h=
7
22
×(1)
2
×16=
7
22
×16=50.29 cm
3

Step 2: Volume of One Cone

Volume
cone
=
1
3
π
r
2
h
=
1
3
×
22
7
×
(
1
)
2
×
1.2
=
1
3
×
22
7
×
1.2
=
1.257

cm
3
Volume
cone
=
3
1
πr
2
h=
3
1
×
7
22
×(1)
2
×1.2=
3
1
×
7
22
×1.2=1.257 cm
3

But for two cones:

Total volume of cones
=
2
×
1.257
=
2.514

cm
3
Total volume of cones=2×1.257=2.514 cm
3

Step 3: Total Volume

Total volume
=
Volume
cylinder
+
Total volume of cones
Total volume=Volume
cylinder
+Total volume of cones
=
50.29
+
2.514
=
52.8

cm
3
=50.29+2.514=52.8 cm
3

Final Answer:

The volume of the pencil is 52.8 cm³.

rhemahills:
To find the volume of the pencil, which consists of a central cylinder and two cones (one at each end), we use the following data from your diagram:

Length of the cylindrical part: 16 cm

Radius of the pencil: 1 cm

Length of each cone: 1.2 cm

Use
π
=
22
7
π=
7
22


Step 1: Volume of the Cylinder

Volume
cylinder
=
π
r
2
h
=
22
7
×
(
1
)
2
×
16
=
22
7
×
16
=
50.29

cm
3
Volume
cylinder
=πr
2
h=
7
22
×(1)
2
×16=
7
22
×16=50.29 cm
3

Step 2: Volume of One Cone

Volume
cone
=
1
3
π
r
2
h
=
1
3
×
22
7
×
(
1
)
2
×
1.2
=
1
3
×
22
7
×
1.2
=
1.257

cm
3
Volume
cone
=
3
1
πr
2
h=
3
1
×
7
22
×(1)
2
×1.2=
3
1
×
7
22
×1.2=1.257 cm
3

But for two cones:

Total volume of cones
=
2
×
1.257
=
2.514

cm
3
Total volume of cones=2×1.257=2.514 cm
3

Step 3: Total Volume

Total volume
=
Volume
cylinder
+
Total volume of cones
Total volume=Volume
cylinder
+Total volume of cones
=
50.29
+
2.514
=
52.8

cm
3
=50.29+2.514=52.8 cm
3

Final Answer:

The volume of the pencil is 52.8 cm³.

rhemahills:
To find the volume of the pencil, which consists of a central cylinder and two cones (one at each end), we use the following data from your diagram:

Length of the cylindrical part: 16 cm

Radius of the pencil: 1 cm

Length of each cone: 1.2 cm

Use
π
=
22
7
π=
7
22


Step 1: Volume of the Cylinder

Volume
cylinder
=
π
r
2
h
=
22
7
×
(
1
)
2
×
16
=
22
7
×
16
=
50.29

cm
3
Volume
cylinder
=πr
2
h=
7
22
×(1)
2
×16=
7
22
×16=50.29 cm
3

Step 2: Volume of One Cone

Volume
cone
=
1
3
π
r
2
h
=
1
3
×
22
7
×
(
1
)
2
×
1.2
=
1
3
×
22
7
×
1.2
=
1.257

cm
3
Volume
cone
=
3
1
πr
2
h=
3
1
×
7
22
×(1)
2
×1.2=
3
1
×
7
22
×1.2=1.257 cm
3

But for two cones:

Total volume of cones
=
2
×
1.257
=
2.514

cm
3
Total volume of cones=2×1.257=2.514 cm
3

Step 3: Total Volume

Total volume
=
Volume
cylinder
+
Total volume of cones
Total volume=Volume
cylinder
+Total volume of cones
=
50.29
+
2.514
=
52.8

cm
3
=50.29+2.514=52.8 cm
3

Final Answer:

The volume of the pencil is 52.8 cm³.

Respects

sirAmeh:
I need help with this Mathematics question

From the diagram, the pencil has 2 Cones and one Cylinder,
diameter = 1 cm, therefore radius = 0.5 cm, π = 22/7

Volume of a Cone = 1/3 πr²h

Where r = 0.5 cm, height h = 1.2 cm

Vol. Cone = 1/3 * 22/7 * 0.5 * 0.5 * 1.2 cm

= 0.314 cm³

Since there are 2 Cones,
Volume of 2 Cones = 2 X 0.314 = 0.628 cm³
= 0.63 cm³

Volume of Cylinder = π r²h

where r = 0.5 cm, h = 16 cm

Volume of Cylimber= πr²h

Volume of Cylinder = 22/7 X 0.5 X 0.5 X 16
= 88/7
= 12:57cm³

Total Volume of pencil = volume of cones + volume of Cylinder = 0.63 cm³ + 12.57cm³
= 13.2cm³

Cc: sirAmeh