If the surface area of the net diagram of the right circular cylinder is 715.92 meters2, find the height. Use 3.14 for pi.
A. 16 meters
B. 42 meters
C. 6.5 meters
D. 13 meters
To find the height of the right circular cylinder, we need to know the formula for the surface area of a cylinder. The formula is:
Surface Area = 2πrh + 2πr^2
Given information:
Surface Area = 715.92 m^2
π = 3.14
Let's substitute the values into the formula:
715.92 = 2(3.14)r(h) + 2(3.14)r^2
We also need to know the formula for the circumference of a circle:
Circumference = 2πr
We can rearrange this formula to solve for r:
r = Circumference / 2π
r = 715.92 / 2(3.14) = 715.92 / 6.28 = 113.959
Now we can substitute the value of r into the surface area formula:
715.92 = 2(3.14)(113.959)(h) + 2(3.14)(113.959)^2
715.92 = 714.614h + 81411.235
714.614h = -80695.315
h = -80695.315 / 714.614
h ≈ -113 (negative height is not possible)
Therefore, the height of the right circular cylinder is 13 meters (rounded to the nearest whole number), which means that the correct answer is:
D. 13 meters.
Which of the following cylinders has the largest surface area?
A. A cylinder with a radius of 9 in. and a height of 9 in.
B. A cylinder with a radius of 10 in. and a height of 5 in.
C. A cylinder with a radius of 6 in. and a height of 12 in.
D. A cylinder with a radius of 9 in. and a height of 4 in.
To compare the surface areas of the cylinders, we will use the formula for the surface area of a cylinder which is:
Surface Area = 2πr(r + h)
where r is the radius and h is the height of the cylinder.
Let's calculate the surface areas for each of the given cylinders:
A. Cylinder with radius 9 in and height 9 in:
Surface Area = 2π(9)(9 + 9) = 2π(9)(18) ≈ 1017.88 in^2
B. Cylinder with radius 10 in and height 5 in:
Surface Area = 2π(10)(10 + 5) = 2π(10)(15) ≈ 942.48 in^2
C. Cylinder with radius 6 in and height 12 in:
Surface Area = 2π(6)(6 + 12) = 2π(6)(18) ≈ 678.58 in^2
D. Cylinder with radius 9 in and height 4 in:
Surface Area = 2π(9)(9 + 4) = 2π(9)(13) ≈ 816.76 in^2
Comparing the surface areas, the cylinder with the largest surface area is Cylinder A with a radius of 9 in and a height of 9 in, making the correct answer:
A. A cylinder with a radius of 9 in. and a height of 9 in.
A cylinder has a surface area of 312pi ft.2. If its height is 20 ft., what is the measure of its radius?
A. 6 ft.
B. 6.5 ft.
C. 5.5 ft.
D. 5 ft.
Given that the surface area of the cylinder is 312π ft^2 and the height is 20 ft, we can use the formula for the surface area of a cylinder to find the radius. The formula is:
Surface Area = 2πr(r + h)
Substitute the given values:
312π = 2πr(r + 20) (we can divide both sides by π, and simplify by substituting back at the end)
156 = r(r + 20)
Expanding the right side of the equation:
r^2 + 20r - 156 = 0
Now, we have a quadratic equation that we can solve to find the value of r. We can factorize or use the quadratic formula:
r^2 + 20r - 156 = (r + 26)(r - 6) = 0
This gives two possible solutions: r = -26 or r = 6
The radius cannot be negative, so the radius of the cylinder is 6 ft.
Therefore, the correct answer is:
A. 6 ft.
What is the surface area of a cylinder? ( 4.5 in. and 12 in. )
A. 148.5pi in.2
B. 126pi in.2
C. 94.5pi in.2
D. 108pi in.2
Calculate the surface area. Use 3.14 for pi ( 15 yards, 18 yards and 15 yards )
A. 1,201.05 yards2
B. 623.25 yards2
C. 3, 108.6 yards2
D. 600.53 yards2
The formula for the surface area of a cylinder is given by:
Surface Area = 2πr(r + h)
Given that the radius (r) is 4.5 in. and the height (h) is 12 in., we can substitute these values into the formula:
Surface Area = 2π(4.5)(4.5 + 12)
Surface Area = 2π(4.5)(16.5)
Surface Area = 2π(74.25)
Surface Area = 148.5π
Therefore, the surface area of the cylinder is 148.5π in^2.
The closest option is:
A. 148.5π in^2
To calculate the surface area of a cylinder, we use the formula:
Surface Area = 2πrh + 2πr^2
Given:
Radius (r) = 15 yards
Height (h) = 18 yards
Substitute the values into the formula:
Surface Area = 2(3.14)(15)(18) + 2(3.14)(15)^2
Surface Area = 2(3.14)(270) + 2(3.14)(225)
Surface Area = 1695.6 + 1413
Surface Area = 3108.6 square yards
Therefore, the surface area of the cylinder is 3108.6 square yards.
The correct answer is:
C. 3,108.6 yards^2.