7. What is the surface area of a conical grain storage tank that has a height of 24 meters and a diameter of 16 meters? Round the answer to the nearest square meter. (1 point)
837 square meters
848 square meters
1,991 square meters
1,923 square meters
8. The lateral area of a cone is 574picm2. The radius is 29 cm. What is the slant height to the nearest tenth of a centimeter? (1 point)
9.9 cm
6.3 cm
19.8 cm
12.6 cm
http://www.calculatorsoup.com/calculators/geometry-solids/cone.php
Not clear if we want only the lateral surface area or the area including the base.
Including the base does not make a not of sense in a storage container for grain, but ...
LSA = πrl, where l is the slant height
l^2 = 24^2 + 8^2
l = √640
LSA = π(8)√640
= appr 635.81 ---> not one of the choices
so let's add the base area, which 64π or 201.06
for a total of 836.88
I see 837
2nd question:
What's the second ?
What’s the second answe?
To find the slant height of a cone with lateral area of 574 \pi \, cm^2 and a radius of 29 cm, we recall that the lateral area of a cone is given by
A_L=\pi rl
where l is the slant height of the cone.
Thus, l= \frac{A_L}{\pi r} = \frac{574\pi}{29\pi} \approx 19.79 \, cm
that's the answer to the second question
To find the surface area of a conical grain storage tank, you need to calculate the lateral area and the base area.
For question 7, the surface area is the sum of the lateral area and the base area.
1. Calculate the lateral area:
The formula for the lateral area of a cone is given by L = πrℓ, where r is the radius and ℓ is the slant height of the cone.
In this case, the radius is half the diameter, so r = 16/2 = 8 meters.
Since the slant height is not given, we need to use the Pythagorean theorem to find it. The slant height is the hypotenuse of a right triangle with the height and the radius as the other two sides.
Using the Pythagorean theorem, we have ℓ^2 = h^2 + r^2, where h is the height.
Substituting the values, we have ℓ^2 = 24^2 + 8^2 = 784 + 576 = 1360.
Taking the square root of both sides, we get ℓ ≈ 36.9 meters (rounded to the nearest tenth).
Now we can calculate the lateral area L:
L = πrℓ = π(8)(36.9) ≈ 925.3 square meters (rounded to the nearest tenth).
2. Calculate the base area:
The base of a cone is a circle, and the area of a circle is given by A = πr^2, where r is the radius.
The base area is A = π(8)^2 = 64π square meters.
3. Calculate the surface area:
Surface area = lateral area + base area = 925.3 + 64π ≈ 925.3 + 201.1 ≈ 1126.4 square meters.
Therefore, the surface area of the conical grain storage tank is approximately 1126.4 square meters. Rounding to the nearest square meter gives the answer as 1,126 square meters. Therefore, the correct answer for question 7 is "1,126 square meters."
Now let's move on to question 8.
For question 8, to find the slant height of the cone, you need to rearrange the formula for the lateral area:
L = πrℓ
Given the lateral area L as 574π square cm and the radius r as 29 cm, rearrange the formula as:
ℓ = L / (πr)
ℓ ≈ 574π / (π * 29) ≈ 574 / 29
ℓ ≈ 19.8 cm
Therefore, the slant height is approximately 19.8 cm. Hence, the correct answer for question 8 is "19.8 cm".