The sum of the height and the radius of a solid cylinder is 35 cm and its total surface area is 3080 cm square . find the valume of the cylinder
Answers
Answer:
It is given that,the sum of the height and the radius of a solid cylinder is 35 cm, mathematically it can be expressed as :
r + h = 35
[ Where, r is the radius of solid cylinder and h is the height of solid cylinder ]
First of all we need to find the radius and height of the solid cylinder :
→ Total surface area of cylinder = 2πr(r + h)
→ 3080 = 2 × 22/7 × r × 35
→ 3080 = 2 × 22 × 5 × r
→ 3080 ÷ 44 = 5r
→ 70 = 5r
→ r = 70 ÷ 5
→ r = 14 cm
Hence,the radius of solid cylinder is 14 cm.
Let's find the height of the cylinder :
→ r + h = 35
→ 14 + h = 35
→ h = 35 - 14
→ h = 21 cm
Hence,the height of solid cylinder is 21 cm.
Now, calculate the volume of cylinder :
→ Volume of cylinder = πr²h
→ Volume of cylinder = 22/7 × (14)² × 21
→ Volume of cylinder = 22 × 2 × 14 × 21
→ Volume of cylinder = 12,936 cm³
Hence,the volume of cylinder is 12,936 cm³.
Answer:
It is given that,the sum of the height and the radius of a solid cylinder is 35 cm, mathematically it can be expressed as :
r + h = 35
[ Where, r is the radius of solid cylinder and h is the height of solid cylinder ]
First of all we need to find the radius and height of the solid cylinder :
→ Total surface area of cylinder = 2πr(r + h)
→ 3080 = 2 × 22/7 × r × 35
→ 3080 = 2 × 22 × 5 × r
→ 3080 ÷ 44 = 5r
→ 70 = 5r
→ r = 70 ÷ 5
→ r = 14 cm
Hence,the radius of solid cylinder is 14 cm.
Let's find the height of the cylinder :
→ r + h = 35
→ 14 + h = 35
→ h = 35 - 14
→ h = 21 cm
Hence,the height of solid cylinder is 21 cm.
Now, calculate the volume of cylinder :
→ Volume of cylinder = πr²h
→ Volume of cylinder = 22/7 × (14)² × 21
→ Volume of cylinder = 22 × 2 × 14 × 21
→ Volume of cylinder = 12,936 cm³
Hence,the volume of cylinder is 12,936 cm³.