To find the volume of a barrel, we can use the formula:
Volume = π * r^2 * h
where r is the base radius and h is the height.
Given that the base radius is 14 and the height is 33, we can substitute these values into the formula:
Volume = π * 14^2 * 33
= π * 196 * 33
= 20484π
So, the volume of the barrel is 20,484π cubic units.
To find the surface area of the barrel, we can break it down into three parts: the curved surface area, the top and bottom circles.
The curved surface area can be calculated using the formula:
Curved Surface Area = 2π * r * h
Given that the base radius is 14 and the height is 33, we can substitute these values into the formula:
Curved Surface Area = 2π * 14 * 33
= 924π
The surface area of the top and bottom circles can be calculated using the formula:
Circle Area = π * r^2
Given that the base radius is 14, we can substitute this value into the formula:
Circle Area = π * 14^2
= 196π
Since there are two circles (top and bottom), we multiply the circle area by 2:
Surface Area of the top and bottom circles = 2 * 196π
= 392π
The total surface area of the barrel is the sum of the curved surface area and the surface area of the top and bottom circles:
Surface Area = Curved Surface Area + Surface Area of the top and bottom circles
= 924π + 392π
= 1316π
So, the surface area of the barrel is 1316π square units.
Find the volume and the surface of the barrel with base radius 14 and a height of 33
1 answer