A cylindrical tube open at both ends is made of metal. The internal diameter of the tube is 11.2 cm and its length is 21 cm. The metal every where is 0.4 cm thick. Calculate the volume of the metal correct to 1 place of decimal
Outer Dia. = 11.2 + 2*0.4 = 12 cm.
V = pi*r^2 * h.
V = 3.14*6^2 * 21 = 2373.8 cm^3.
To calculate the volume of the metal, we first need to find the volume of the outer cylinder and then subtract the volume of the inner cylinder.
1. Calculate the radius of the outer cylinder:
The diameter is given as 11.2 cm, so the radius (r) is half of the diameter:
r = 11.2 cm / 2 = 5.6 cm.
2. Calculate the volume of the outer cylinder:
The volume of a cylinder is given by the formula V = πr^2h, where π is a constant (approximately 3.14159), r is the radius, and h is the height (or length) of the cylinder.
V_outer = π × (r + thickness)^2 × h
= π × (5.6 cm + 0.4 cm)^2 × 21 cm
3. Calculate the radius of the inner cylinder:
The inner radius is the outer radius minus the thickness:
r_inner = r - thickness
= 5.6 cm - 0.4 cm
4. Calculate the volume of the inner cylinder:
V_inner = π × r_inner^2 × h
= π × (5.6 cm - 0.4 cm)^2 × 21 cm
5. Calculate the volume of the metal:
V_metal = V_outer - V_inner
Now, let's calculate the values step by step:
Step 1:
r = 5.6 cm
Step 2:
V_outer = π × (5.6 cm + 0.4 cm)^2 × 21 cm
Step 3:
r_inner = 5.6 cm - 0.4 cm
Step 4:
V_inner = π × (5.6 cm - 0.4 cm)^2 × 21 cm
Step 5:
V_metal = V_outer - V_inner
Calculate the values accordingly and subtract V_inner from V_outer to find V_metal. Round the final answer to 1 decimal place.