An open (hollow) cylindrical barrel has a base radius 14 cm and a height of 33cm
A) find the volume and the surface area of the barrel.
B) if a fly is at the point on the bottom inner rim of the barrel, how much distance (minimum) will it have to travel to reach the farthest point on the barrel?
C)if a ant is at the point on the bottom inner rim of the barrel, how much distance (minimum) will it have to travel to reach the farthest point on the barrel?
first of all whosoever came to this site to check the answer please don't do so as it gives totally wrong answer...in the first place the answer to the fly question is totally wrong without any logic or anything so I would like to say that if you want the real answer it will be that if applied like travels from the diagonal it will be the father's distance forms of Pythagoras theorem write a right angle triangle in which the base of given and the height is given and the hypertonicity to calculate that will be there for the distance for fly that's the actual procedure to do that sum so it will be Root over 28 square + 33square and its answer with will give you around 43 approx
A) To find the volume of the barrel, you can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
where π is a constant approximately equal to 3.14159, r is the base radius of the barrel, and h is the height of the barrel.
Substituting the given values, we have:
Volume = π * (14 cm)^2 * 33 cm
= 3.14159 * 196 cm^2 * 33 cm
≈ 204331.67 cm^3
To find the surface area of the barrel, you can use the formula for the lateral surface area of a cylinder:
Surface Area = 2 * π * r * h
Substituting the given values, we have:
Surface Area = 2 * 3.14159 * 14 cm * 33 cm
≈ 29179.78 cm^2
Therefore, the volume of the barrel is approximately 204331.67 cm^3 and the surface area is approximately 29179.78 cm^2.
B) To find the minimum distance the fly will have to travel to reach the farthest point on the barrel, we can use the concept of the diameter of the circle. The diameter is the longest distance between any two points on a circle.
In this case, the diameter of the circular base of the barrel is equal to twice the radius, which is 2 * 14 cm = 28 cm. Therefore, the minimum distance the fly will have to travel to reach the farthest point on the barrel is equal to the diameter, which is 28 cm.
C) The ant, being on the inner rim of the barrel, would need to travel along the curved surface of the barrel to reach the farthest point. Since the inner rim is a circle, the distance along the curved surface can be calculated using the circumference formula:
Distance = 2 * π * r
Substituting the given value of the radius, we have:
Distance = 2 * 3.14159 * 14 cm
≈ 87.9646 cm
Therefore, the minimum distance the ant will have to travel to reach the farthest point on the barrel is approximately 87.9646 cm.
A) To find the volume of the barrel, we can use the formula for the volume of a cylinder, which is given by V = πr^2h, where π is a mathematical constant approximately equal to 3.14159, r is the base radius, and h is the height.
In this case, the base radius (r) is 14 cm and the height (h) is 33 cm. Substituting these values into the formula, we get:
V = π * (14 cm)^2 * 33 cm
To find the surface area of the barrel, we need to consider both the curved surface area and the base areas. The curved surface area can be calculated using the formula A_curved = 2πrh, and the base areas can be determined using the formula A_base = πr^2.
To calculate the total surface area, we sum the curved surface area and the base areas. The formula for the total surface area (A_total) is given by:
A_total = A_curved + 2A_base
B) To determine the minimum distance the fly needs to travel to reach the farthest point on the barrel, we can consider the diagonal of the rectangle formed by the base radius and the height. Using the Pythagorean theorem, the diagonal (d) can be calculated as follows:
d = √(r^2 + h^2)
C) Finding the minimum distance the ant needs to travel is similar to the fly's scenario. However, since the ant is much smaller than the fly, it can crawl along the inner rim of the barrel. Therefore, the ants' minimum distance is the same as the circumference of the inner rim of the barrel.
A) To find the volume of the barrel, we can use the formula V = πr^2h, where r is the base radius and h is the height.
V = π(14 cm)^2(33 cm)
V ≈ 20045.0418 cm^3
To find the surface area, we can use the formula A = 2πrh + 2πr^2.
A = 2π(14 cm)(33 cm) + 2π(14 cm)^2
A ≈ 4155.3127 cm^2
B) The farthest point on the barrel from the bottom inner rim is the topmost point on the outer rim. To calculate the minimum distance the fly has to travel, we can use the circumference formula C = 2πr, where r is the base radius.
C = 2π(14 cm)
C ≈ 87.9646 cm
C) Similarly, the farthest point on the barrel from the bottom inner rim is the topmost point on the outer rim. To calculate the minimum distance the ant has to travel, we can use the curved surface distance of the barrel, which is the circumference of the outer rim.
C = 2π(14 cm)
C ≈ 87.9646 cm
So, the minimum distance the ant has to travel is approximately 87.9646 cm.
why are B and C the same?
v = πr^2h = 6468π cm^3
a = πr^2 + 2πrh = 1120π cm^2
As for the distance, the most obvious answer is to go right across the bottom and straight up, for a distance of 28+33=61 cm.
To figure minimum distance, you have to find the length of 1/2 of a turn of a helix of radius 14 and length 66: 54.99 cm.