A solid cone of base radius 5cm and height 6cm IDs made of metal of density 4g/cm cubed, calculate it's mass
Mass = (1/3)πr2h x density
Mass = (1/3)π(5cm)2(6cm) x 4g/cm3
Mass = (1/3)π(25cm2) x 4g/cm3
Mass = (1/3)π(100cm3) x 4g/cm3
Mass = (1/3) x 3.14 x 400g
Mass = 400g
Interesting that the bot cannot do simple arithmetic ...
Mass = (1/3) π (25)(6)(4) g
= 200π g
or
appr 628.3 g
To calculate the mass of the solid cone, we need to find its volume and then multiply it by its density.
The volume of a cone can be calculated using the formula:
V = (1/3)πr^2h
Given:
Base radius, r = 5 cm
Height, h = 6 cm
Substituting these values in the formula, we get:
V = (1/3)π(5^2)(6)
V = (1/3)π(25)(6)
V = (1/3)(25π)(6)
V = 50π cm^3
The density of the metal is given as 4 g/cm^3.
Now we can calculate the mass:
Mass = Volume × Density
Mass = 50π cm^3 × 4 g/cm^3
Mass = 200π g
So, the mass of the solid cone is 200π grams.
To calculate the mass of the solid cone, we need to know its volume and the density of the material it is made of. The formula to calculate the volume of a cone is given by V = (1/3) * π * r^2 * h, where V is the volume, π is a constant (approximately 3.14), r is the radius of the base, and h is the height.
Given:
Base radius (r) = 5 cm
Height (h) = 6 cm
Density (ρ) = 4 g/cm³
Let's calculate the volume of the solid cone first:
V = (1/3) * π * r^2 * h
= (1/3) * 3.14 * 5^2 * 6
≈ 157 cm³
Now that we have the volume, we can calculate the mass using the formula:
Mass (m) = Volume (V) * Density (ρ)
m = V * ρ
= 157 cm³ * 4 g/cm³
= 628 g
Therefore, the mass of the solid cone is approximately 628 grams.