height of a right circular cone filled with sand is 9 cm. radius of the base of the cone is 3.5cm. find the mass of sand@10g per cm3
10g/cm^3 * 1/3 π*3.5^2*9 cm^3 = ? g
To find the mass of the sand in the cone, we need to calculate the volume of the cone first and then multiply it by the density of the sand.
The volume of a right circular cone can be calculated using the formula:
V = (1/3) * π * r² * h
Where:
V = Volume of the cone,
π = Pi (approximately 3.14159),
r = Radius of the base of the cone,
h = Height of the cone.
Given:
r = 3.5 cm
h = 9 cm
Substitute the given values into the formula:
V = (1/3) * 3.14159 * (3.5)² * 9
Simplifying the equation:
V = (1/3) * 3.14159 * 12.25 * 9
V = 37.6991 cm³ (rounded to four decimal places)
Now, we can calculate the mass of the sand by multiplying the volume (V) by the density (d).
Given:
d = 10 g/cm³ (density of sand)
Mass = V * d
Substitute the values into the equation:
Mass = 37.6991 cm³ * 10 g/cm³
Mass = 376.991 g (rounded to three decimal places)
Therefore, the mass of the sand in the cone is approximately 376.991 grams.