calculate the volume and total sarface area of right circular cylinder of height 1m and radius 70cm
Radius, r = 70 cm
Height, h = 1 m = 100 cm (convert to cm for ease of calculation)
Volume of cylinder = πr²h
= π(70)²(100)
= 1,539,380 cm³
Total surface area of cylinder = 2πr² + 2πrh
= 2π(70)² + 2π(70)(100)
= 30,935.8 cm² + 43,982.3 cm²
= 74,918.1 cm²
Therefore, the volume of the cylinder is 1,539,380 cm³ and the total surface area is 74,918.1 cm².
A glass cylinder with a radius of 7cm has water up to a height of 9cm. A metal cube of 5½cm edge is immersed in completely. Calculate the height by which the water rises in the cylinder.
The volume of the water displaced by the cube will be equal to the volume of the cube:
Volume of cube = (5.5 cm)³ = 166.375 cm³
Now we can use the equation for volume of a cylinder to find the volume of water initially in the cylinder:
Volume of water in cylinder = πr²h
= π(7 cm)²(9 cm)
= 1385.44 cm³
When the cube is immersed in the water, it will displace a certain amount of water and the water level in the cylinder will rise. Let's call the height by which the water level rises "h".
The volume of water in the cylinder after the cube is immersed will be the same as the initial volume plus the volume of the cube:
Volume of water in cylinder after immersion = Volume of water initially + Volume of cube
= 1385.44 cm³ + 166.375 cm³
= 1551.815 cm³
Now we can use the equation for volume of a cylinder again to find the new height of the water level:
Volume of water in cylinder after immersion = πr²h'
1551.815 cm³ = π(7 cm)²h'
1551.815 cm³ = 1078.097 cm² h'
h' = 1.44 cm
Therefore, the water level in the cylinder will rise by approximately 1.44 cm when the cube is immersed in the water.
To calculate the volume and total surface area of a right circular cylinder, you can use the following formulas:
1. Volume of a cylinder:
The formula to calculate the volume of a cylinder is V = π * r^2 * h, where V is the volume, π is a constant approximately equal to 3.14, r is the radius, and h is the height.
2. Total surface area of a cylinder:
The formula to calculate the total surface area of a cylinder is A = 2πrh + 2πr^2, where A is the total surface area, π is a constant approximately equal to 3.14, r is the radius, and h is the height.
Now, let's calculate the volume and total surface area of the given right circular cylinder.
Given:
Height (h) = 1 meter
Radius (r) = 70 cm = 0.7 meter
1. Volume:
V = π * r^2 * h
V = 3.14 * (0.7)^2 * 1
V ≈ 1.539 cubic meters
Therefore, the volume of the cylinder is approximately 1.539 cubic meters.
2. Total surface area:
A = 2πrh + 2πr^2
A = 2 * 3.14 * 0.7 * 1 + 2 * 3.14 * (0.7)^2
A ≈ 7.554 + 2.646
A ≈ 10.2 square meters
Therefore, the total surface area of the cylinder is approximately 10.2 square meters.