Question

A company packages its product cylinder container whose base has a diameter of 17.5cm and height 32 cm. Company places a label around the surface of the container. If the label is placed 3cm from the top and 4cm from the bottom, find the area of the label.​

Answer 1

Answer:

$\bigstar{\bold{Area\:of\:label=1373.75\:cm^{2}}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Diameter of cylinder = 17.5 cm
• Height = 32 cm
• Label is placed 3 cm from top and 4 cm from bottom

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The area of the label

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Height of the label = Height of cylinder - 3 -4

  Height of the label = 32 - 3 - 4

  Height of label = 25 cm

→ Diameter of label = Diameter of cylinder

  Diameter of label = 17.5 cm

  Radius of label = 17.5/2 = 8.75 cm

→ Area of the label is given by the curved surface area of cylinder

  Area of label = 2 π r h

  where r is radius of label and h is the height of the label

→ Substitute the datas,

  Area of label = 2 × 3.14 × 8.75 × 25

  Area of label = 1373.75 cm²

$\boxed{\bold{Area\:of\:label=1373.75\:cm^{2}}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ Curved surface area of a cylinder is given by the formula,

  CSA = 2 π r h

→ Total surface area of a cylinder is given by the formula,

  TSA = 2 π r ( r + h )

→ Volume of cylinder is given by the formula,

  Volume = π r² h

Answer 2

$\bigstar{\bold{Area\:of\:label=1373.75\:cm^{2}}}$★Areaoflabel=1373.75cm

2

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

Diameter of cylinder = 17.5 cm

Height = 32 cm

Label is placed 3 cm from top and 4 cm from bottom

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

The area of the label

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Height of the label = Height of cylinder - 3 -4

Height of the label = 32 - 3 - 4

Height of label = 25 cm

→ Diameter of label = Diameter of cylinder

Diameter of label = 17.5 cm

Radius of label = 17.5/2 = 8.75 cm

→ Area of the label is given by the curved surface area of cylinder

Area of label = 2 π r h

where r is radius of label and h is the height of the label

→ Substitute the datas,

Area of label = 2 × 3.14 × 8.75 × 25

Area of label = 1373.75 cm²

$\boxed{\bold{Area\:of\:label=1373.75\:cm^{2}}}$

Areaoflabel=1373.75cm

2

$\Large{\underline{\underline{\bf{Notes:}}}}$

Notes:

→ Curved surface area of a cylinder is given by the formula,

CSA = 2 π r h

→ Total surface area of a cylinder is given by the formula,

TSA = 2 π r ( r + h )

→ Volume of cylinder is given by the formula,

Volume = π r² h