Question

the total surface area of a right circular cylinder is 880cm^2 and its diameter is 14 cm. find its height and volume.​

Answer 1

Answer:

Height of the cylinder is 13 cm and the volume of the cylinder is 2002 cm³.

Step-by-step explanation:

Given :-

• The total surface area of a right circular cylinder is 880 cm².
• Its diameter is 14 cm.

To find :-

• Its height and volume.

Solution :-

Consider,

• Height of the cylinder = h cm

Diameter of the cylinder = 14 cm

Then,

• Radius of the cylinder(r) = 14/2 = 7 cm

Formula used :-

${\boxed{\sf{TSA\:of\: cylinder=2\pi\:r(h+r)}}}$

★ TSA of cylinder is 880 cm².

According to the question,

2πr(h+r)=880

→ 2 × (22/7) × 7 (h+7) = 880

→ 44 (h+7) = 880

→ h+7 = 880/44

→ h+7 = 20

→ h = 20-7

→ h = 13

Therefore the height of the cylinder is 13 cm.

Formula used :-

${\boxed{\sf{Volume\:of\: cylinder=\pi\:r^2h}}}$

Volume of the cylinder,

= πr²h

= (22/7)×7×7×13 cm³

= 22 × 7 × 13 cm³

= 2002 cm³

Therefore the volume of the cylinder is 2002 cm³

Answer 2

Explanation :-

Given :-

• The total surface area of a right circular cylinder = 880cm².
• It's diameter is 14cm.

To Find :-

• It's height and volume.

Solution :-

Radius = Diameter / 2

=> Radius = 14/2

=> Radius = 7cm.

__________________

Find the height of right circular cylinder.

As we know that,

Total surface area of cylinder = 2πr(h+r)

=> 880 = 2 × 22/7 × 7(h + 7)

=> 880 = 44 × (h + 7)

=> 880/44 = h + 7

=> 20 = h + 7

=> h = 20 - 7

=> h = 13cm.

__________________

Now, find the Volume of right circular cylinder.

Volume of cylinder = πr²h

=> Volume of cylinder = 22/7 × (7)² × 13

=> Volume of cylinder = 22 × 7 × 13

=> Volume of cylinder = 154 × 13

=> Volume of cylinder = 2002cm³.