7. What is the surface are of a conical grain storage tank that has a height of 37 meters and a diameter of 16 meters? Round the answer to the nearest square meter.

2,831 square meters
2,664 square meters
1,152 square meters
1,131 square meters

Thank You!

To find the surface area of a conical grain storage tank, we need to calculate the curved surface area of the conical part.

The formula to calculate the curved surface area of a cone is given by:
Surface Area = πrℓ, where r is the radius of the base and ℓ is the slant height.

First, let's find the radius of the base. The diameter is given as 16 meters, so the radius (r) can be found by dividing the diameter by 2:
r = 16 / 2 = 8 meters.

Next, we need to find the slant height (ℓ). Using the height (h) and the radius (r), we can use the Pythagorean theorem:
ℓ = √(r^2 + h^2) = √(8^2 + 37^2) = √(64 + 1369) = √1433 ≈ 37.88 meters (rounded to two decimal places).

Now that we have the radius (r = 8 meters) and the slant height (ℓ ≈ 37.88 meters), we can calculate the curved surface area:
Surface Area = πrℓ ≈ π(8)(37.88) ≈ 237.6π square meters.

To round the answer to the nearest square meter, we need to calculate the value of π. Using the approximation π ≈ 3.14, we can find the approximate surface area:
Surface Area ≈ 237.6(3.14) ≈ 745.824 square meters.

Rounding this value to the nearest square meter, we get:
Surface Area ≈ 746 square meters.

Therefore, the correct answer is: 746 square meters.

To find the surface area of a conical grain storage tank, you need to calculate the lateral surface area and the base area separately, and then add them together.

The lateral surface area of a cone can be calculated using the formula A = πrℓ, where A is the area, π is a mathematical constant (approximately 3.14159), r is the radius, and ℓ is the slant height.

To find the slant height, we can use the Pythagorean theorem. The slant height forms a right triangle with the height (h) and the radius (r) as the legs.

In this case, the height of the cone is given as 37 meters and the diameter is given as 16 meters. To find the radius, we divide the diameter by 2, giving us a radius of 8 meters.

Next, we can find the slant height using the Pythagorean theorem:

slant height (ℓ) = √(r^2 + h^2)
ℓ = √(8^2 + 37^2)
ℓ = √(64 + 1369)
ℓ ≈ √1433
ℓ ≈ 37.87 meters

Now that we have the radius and slant height, we can calculate the lateral surface area:

lateral surface area = π * r * ℓ
lateral surface area = 3.14159 * 8 * 37.87
lateral surface area ≈ 941.47 square meters (rounded to two decimal places)

The base area of a cone is simply the area of a circle, which can be calculated using the formula A = πr^2.

base area = π * r^2
base area = 3.14159 * (8)^2
base area ≈ 201.06 square meters (rounded to two decimal places)

Finally, we can calculate the total surface area by summing the lateral surface area and the base area:

total surface area = lateral surface area + base area
total surface area ≈ 941.47 + 201.06
total surface area ≈ 1,142.53 square meters (rounded to two decimal places)

Therefore, the surface area of the conical grain storage tank is approximately 1,143 square meters. None of the given options are correct.

let the slant height be s

s^2 = 8^2 + 37^2
s = 37.8549..

Lateral surface area = πrs
= π(8)(37.8549..)
= appr 9514 , none of the given choices

if we include the circular base of 201.062

we get appr 1152 m^2