Question

A tent of height 33 cm is in the form of a right circular cylinder of diameter 42 cm and height 5 cm surmounted by a right circular cone of the same diameter. Find the total surface area of the tent. I tried this question but there is some mistak
.. I guess. The answer is 2970 cm Sq. plz check my answer and correct it. ​

Answer 1

Given :

A tent of height 33 cm is in the form of a right circular cylinder of diameter 42 cm and height 5 cm surmounted by a right circular cone of the same diameter.

To Find :

The total surface area of the tent.

Solution :

Analysis :

Here the formula of curved surface area of cylinder and cone is used. Here we first have to find the radius from the diameter of the cylinder. Then using the total height of the tent we can find the height of the cone.For the total surface area we have to add up the curved surface area of cylinder and cone.

Required Formula :

• Curved Surface Area of Cylinder = 2πrh

• Curved Surface Area of Cone = πrl

where,

• r = Radius
• h = Height
• l = Slant Height

Explanation :

Curved Surface Area of Cylinder :

We know that,

Radius = Diameter/2

⇒ 42/2

⇒ 21

∴ Radius of cylinder = 21 cm.

We know that if we are given the radius, height of the cylinder and is asked to find the Curved Surface Area of Cylinder then our required formula is,

Curved Surface Area of Cylinder = 2πrh

where,

• π = 22/7
• r = 21 cm
• h = 5 cm

Using the required formula and substituting the required values,

⇒ CSA = 2πrh

⇒ CSA = 2 × 22/7 × 21 × 5

⇒ CSA = 2 × 22 × 3 × 5

⇒ CSA = 660

∴ Curved Surface Area of Cylinder = 660 cm².

Curved Surface Area of Cone :

We are given that the height of the whole tent is 33 cm.

Height of the cylinder = 5 cm

Height of cone = Total Height - Height if cylinder

= 33 - 5

= 28

∴ Height of the cone = 28 cm.

We know that if we are given the radius, height of the cylinder and is asked to find the Curved Surface Area of Cylinder then our required formula is,

Curved Surface Area of Cone = πrl

where,

• π = 22/7
• r = 21 cm

For the slant height(l),

We know that,

l = √[r² + h²]

where,

• l = Slant Height
• r = Radius = 21 cm
• h = Height = 28 cm

Using the required formula and substituting the required values,

⇒ l = √[r² + h²]

⇒ l = √[(21)² + (28)²]

⇒ l = √[441 + 784]

⇒ l = √[1225]

⇒ l = √[35 × 35]

⇒ l = 35

∴ Slant Height = 35 cm.

Now,

Curved Surface Area of Cone = πrl

where,

• π = 22/7
• r = 21 cm
• l = 35 cm

Using the required formula and substituting the required values,

⇒ CSA = πrl

⇒ CSA = 22/7 × 21 × 35

⇒ CSA = 22 × 3 × 35

⇒ CSA = 2310

∴ Curved Surface Area of Cone = 2,310 cm².

Total Surface Area of tent :

Total Surface Area of Tent = Curved Surface Area of Cylinder + Curved Surface Area of Cone

where,

• Curved Surface Area of Cylinder = 660 cm²
• Curved Surface Area of Cone = 2,310 cm²

Using the required formula and substituting the required values,

⇒ Total Surface Area of Tent = 660 + 2310

⇒ Total Surface Area of Tent = 2970

∴ Total Surface Area of Tent = 2,970 cm².

Total surface area of the tent is 2,970 cm².