A paper cone has a base diameter of 8 cm and a height of 3 cm calculate the volume of the cone in terms of pipe we make a sketch of the cone and ends use Pythagoras theorem to calculate its slant lines
in calculate the curved surface area of the cone in terms of pi thing if the cone is cut and open out into the sector of a circle what is the angle of the sector
First, we can use Pythagoras theorem to find the slant height of the cone:
s = sqrt(r^2 + h^2) = sqrt(4^2 + 3^2) = 5 cm
where r is half the base diameter (4 cm) and h is the height (3 cm).
Now, we can use the formula for the volume of a cone:
V = (1/3)πr^2h
Substituting the values we have:
V = (1/3)π(4^2)(3) = 16π/3 cm^3
To find the curved surface area of the cone, we use the formula:
A = πrs
where r is the radius of the base (4 cm) and s is the slant height (5 cm). Substituting the values:
A = π(4)(5) = 20π cm^2
If we cut the cone and open it out into a sector of a circle, the angle of the sector will be the same as the angle at the apex of the cone. To find this angle, we can use trigonometry:
tan(θ) = r/h = 4/3
θ = tan^-1(4/3) ≈ 53.13°
Therefore, the angle of the sector is approximately 53.13°.
The table shows climate data for Austin, Texas.
Climate Data for Austin, Texas (1981–2010)
Precipitation (in.) Temperature (ºF)
March 2.51 59
April 2.28 67
May 2.66 75
June 4.38 81
Which statement about the climate in spring in Austin, Texas, is correct?
(1 point)
Responses
The temperature in May is 75ºF every day.
There will be more than 2 inches of rainfall next April.
It always rains more in June than in May.
It is usually warmer in April than in March.
It is usually warmer in April than in March.
Weather and Climate Unit Test
12 of 1312 of 13 Items
Question
A bar graph shows the average temperatures for the first four days in March. The average temperature for each day is listed.
March 1 was 52°F.
March 2 was 54°F.
March 3 was 56°F.
The average temperature for March 4 followed the temperature trend. Which most likely was the temperature on March 4?
(1 point)
Responses
60°F
55°F
50°F
56°F
56°F
Ali says the climate of a town is rainy because it is raining outside today. Is she correct? In one or two sentences, explain why Ali is or is not correct about the climate of the town.
Ali is not correct about the climate of the town. Climate refers to long-term patterns of weather, and weather refers to the current atmospheric conditions at a specific time and place. Just because it is raining on a particular day does not necessarily indicate that the town has a rainy climate overall.
Bats and large snakes live in a steamy rain forest in South America. What best describes the climate in which these animals live?(1 point)
Responses
cold
wet
windy
dry
wet
To calculate the volume of the cone, we can use the formula:
Volume = (1/3) * π * r^2 * h
First, we need to find the radius (r) of the base of the cone. The base diameter is given as 8 cm, so the radius (r) would be half of that, which is 4 cm.
Next, we substitute the values into the formula:
Volume = (1/3) * π * (4 cm)^2 * 3 cm
= (1/3) * π * 16 cm^2 * 3 cm
= (1/3) * π * 48 cm^3
= (16/3) * π cm^3
Therefore, the volume of the cone is (16/3) * π cm^3.
To calculate the curved surface area of the cone, we need to find the slant height (l) first. We can use Pythagoras' theorem to find the slant height.
Pythagoras' theorem: l^2 = r^2 + h^2
Substituting the values:
l^2 = (4 cm)^2 + (3 cm)^2
l^2 = 16 cm^2 + 9 cm^2
l^2 = 25 cm^2
l = √25
l = 5 cm
Now, to find the curved surface area (A) of the cone, we use the formula:
A = π * r * l
Substituting the values:
A = π * (4 cm) * 5 cm
A = 20π cm^2
Therefore, the curved surface area of the cone is 20π cm^2.
Finally, if the cone is cut and opened out into a sector of a circle, the angle of the sector is given by the formula:
Angle = (Curved Surface Area / π * r^2) * 360°
Substituting the values:
Angle = (20π cm^2 / π * (4 cm)^2) * 360°
Angle = (20π cm^2 / π * 16 cm^2) * 360°
Angle = (20/16) * 360°
Angle = 45° * 360°
Angle = 180°
Therefore, the angle of the sector would be 180°.