An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of the base of each of cone and cylinder is 8 cm. The cylinderical part is 240 cm high and the conical part in 36 cm high. Find the weight of the pillar if one cu. cm of iron weighs 7.8 grams.
plz answer me
Answers
Given :
An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone.
- Dimensions of cylinder
★ Radius of cylinder = 8cm
★ Height of cylinder = 240cm
- Dimensions of cone
★ Radius of cone = 8cm
★ Height of cone = 36cm
To find :
- The weight of the pillar if one cm³ of iron weighs 7.8 grams.
Solution :
We need to remember some points before solving such types of problems
- Firstly, we need to find out the volume of the given dimension(s)
- Volume of cylinder = πr²h where, r is radius & h is height
- Volume of cone = ⅓ π²h
According to the given condition
- Volume of cylinder
→ πr²h
→ π × 8 × 8 × 240
→ 64 × 240 × π
→ 15360π cm³
- Volume of cone
→ ⅓ πr²h
→ ⅓ × π × 8 × 8 × 36
→ 64 × 12 × π
→ 768π cm³
Now,
★ Weight of the pillar = Volume of cylinder + volume of cone
→ 15360π + 768π
→ 16128 × 22/7
→ 2304 × 22
→ 50688cm³
★ 1 cm³ of iron weighs 7.8gm
- 1kg = 1000gm
→ Weight of 50688cm³
→ 7.8/1000 × 50688
→ 395366.4/1000
→ 395.3kg
•°• The weight of pillar is 395.3kg
━━━━━━━━━━━━━━━━━━━━━━━━
Given :-
Radius = 8 cm
Height of cylinder = 240 cm
the conical part in 36 cm high.
To Find :-
Weight of the pillar if one cu. cm of iron weighs 7.8 grams.
Solution :-
We know that
Volume of cylinder = πr²h
Volume of cone = ⅓πr²h
Now,
Volume of cylinder = 3.14 × 8 × 8 × 240
=> 48320.4 cm^3
Now
⅓ × 3.14 × 8 × 8 × 36
1 × 3.14 × 8 × 8 × 12
3.14 × 64 ×12
2411.52 cm^3
Now
Weight of pillar = Volume of cylinder + volume of cone
W = 48320.4 + 2411.52
W = 50730
Now
1kg = 1000gm
7.8/1000 × 50730
0.0078 × 50730
395.4 kg