The volume of a cylinder is 448π
cm3 and height 7 cm. Find its lateral surface
surface area and
total surface area.
Answers
Given:
- Volume of Cylinder = 448π
- Height, h = 7 cm
To find out:
Find the lateral surface area and Total surface area.
Formula used:
- Total surface area = 2πr ( h + r )
- Lateral surface area = 2πrh
Solution:
Let the radius of the base be r cm.
✪According to question:-
Volume of cylinder = 448π cm³
⇒ πr²× 7 = 448π cm³
⇒ r² × 7 = 448
⇒ r² = 448/7
⇒ r² = 64
⇒ r = 8 cm
Now,
( i ) Lateral surface area = 2πrh cm²
= 2 × 22/7 × 8 × 7 cm²
= 2 × 22 × 8 cm²
= 352 cm²
( ii ) Total surface area = 2πr( h + r ) cm²
= 2 × 22/7 × 8 ( 7 + 8 ) cm²
= 44/7 × 8 × 15 cm²
= 5280/7 cm²
= 754.28
Given:
- Volume of cylinder = 448π cm³
- Height of cylinder = 7 cm
To find :
- Radius of the cylinder =?
Step-by-step explanation :
We know from the formula of cylinder;
Volume, V = πr²h cubic units
So, 448π = (π) × r² × 7
➮ r² = (448)/(7)
➮ r² = 448/7
➮ r² = 64
➮ r = √64
➮ r = √8 x 8
➮ r = 8.
Therefore, r = 8 cm
Therefore, The radius of a cylinder = 8 cm.
Now,
We have to find the Lateral Surface Area,
Given :
- Radius of cylinder = 8 cm
- Height of cylinder = 7 cm
To find :
- Lateral Surface Area of Cylinder = ?
Step-by-step explanation :
We know that,
Lateral Surface Area of Cylinder = 2π × r × h
Substituting the values in the above formula, we get,
= 2 ( 22 / 7 ) × 8 × 7
= 2 × 22 × 8
= 352.
Therefore, The Lateral Surface Area of Cylinder = 352 cm².
Now,
We have to find the Total Surface Area of Cylinder,
Given :
- Radius of cylinder = 8 cm
- Height of cylinder = 7 cm
To find :
- Total Surface Area of Cylinder =?
Step-by-step explanation :
We know that,
Total Surface Area of Cylinder = 2π×r(r+h)
Substituting the values in the above formula, we get,
= 2 ( 22 / 7 ) × 8 ( 8 + 7 )
= 2 ( 22 / 7 ) × 8 × 15
= 2 × 3.14 × 120
= 753.6
Therefore, Total Surface Area of Cylinder = 753.6 cm².