the ends of the root a woprkshop are segment of a crcle of radius 10metres . the roof is 20metres long the angle of the ciorcle is 120 degrees calculate the area of one end of the roof (b)the area of the curves surface area of the roof (c) what wouid be the the nearest shilling of covering the two ends and the curved surface with galvanised iron heating sh 80 per square metre
To calculate the area of one end of the roof (b), we need to find the area of a sector of a circle. The formula for the area of a sector is (θ/360) * π * r^2, where θ is the angle in degrees and r is the radius.
In this case, the angle of the circle is 120 degrees and the radius is 10 meters. Plugging these values into the formula, we get:
Area of one end (b) = (120/360) * π * 10^2 = (1/3) * π * 100 ≈ 104.72 square meters
To calculate the area of the curved surface of the roof (c), we need to find the area of a circle with a radius of 10 meters, and then subtract the areas of the two ends. The formula for the area of a circle is π * r^2.
Area of curved surface (c) = π * 10^2 - 2 * Area of one end (b)
= π * 100 - 2 * 104.72
≈ 314.16 - 209.44
≈ 104.72 square meters
To calculate the cost of covering the two ends and the curved surface with galvanized iron, we need to multiply the total area by the cost per square meter. In this case, the cost is 80 shillings per square meter.
Total cost = (Area of one end (b) + Area of curved surface (c)) * Cost per square meter
= (104.72 + 104.72) * 80
= 209.44 * 80
≈ 16,755.20 shillings
Therefore, the nearest shilling cost of covering the two ends and the curved surface with galvanized iron is 16,755 shillings.
a cone is made by cutting off a sector as shown below ffrom a cicle and gluing the straIGHT EDGES of the sector the cone formed has a slant height 14cm and circular base of perimeter
a)detgermine the value of tetor
b)the radius of the cone circular base
c)the height of the cone
d)the cone is cut uniformly on a horizontal plane 1cm below the apex calculate the slant height of the frustum so formed
2)a wooden drum clossed at the top and bottom has a top radius of 28cm and bottom radius 21cm its height is 90cm the drum is covered with leather the top and bottom
a)the volumeof the drum in litres
b)the area of the leather covering the drum excluding the top and bottom
a) To determine the value of the sector angle (θ), we can use the slant height (s) and the radius (r) of the circular base of the cone.
Since the slant height (s) is given as 14 cm, and we can consider the radius (r) as the radius of the original circle, we have:
s = r + r = 2r
2r = 14 cm
r = 7 cm
The sector angle (θ) can be found using the formula for the circumference of a circle:
C = 2πr
2πr = θ/360 * 2πr
360 = θ/360 * 360
θ = 360 degrees
b) The radius of the cone circular base is given as 7 cm.
c) Since the cone is made by cutting off a sector from a circle, the height (h) of the cone is the distance between the apex (top point) and the base. This height can be found using the Pythagorean theorem:
h^2 = s^2 - r^2
h^2 = 14^2 - 7^2
h^2 = 196 - 49
h^2 = 147
h = √147 cm
d) To find the slant height of the frustum formed by cutting the cone uniformly on a horizontal plane 1 cm below the apex, we can use the Pythagorean theorem again. The slant height (l) is the hypotenuse of a right triangle with the height (h+1 cm) of the frustum and the radius (r) as the other two sides:
l^2 = (h+1)^2 + r^2
l^2 = (√147 + 1)^2 + 7^2
l^2 = (12 + 1)^2 + 7^2
l^2 = 13^2 + 7^2
l^2 = 169 + 49
l^2 = 218
l = √218 cm
a) To calculate the volume of the drum in liters, we can use the formula for the volume of a cylinder:
V = πr^2h
V = π(28^2 - 21^2)(90) = π(784 - 441)(90) = π(343)(90) = 9639π cm³
Since we want the volume in liters, we divide by 1000 (since 1 liter = 1000 cm³):
V = (9639π) / 1000 ≈ 30.26 liters
b) To calculate the area of the leather covering the drum excluding the top and bottom, we find the lateral surface area of the drum.
The lateral surface area (A) of a cylinder can be calculated using the formula:
A = 2πrh, where r is the radius of the drum and h is the height.
A = 2π(21)(90) + 2π(28)(90) = 3780π + 5040π = 8820π cm²
Since we want the area in square meters, we divide by 10000:
A = (8820π) / 10000 ≈ 2.77 m²
Therefore, the area of the leather covering the drum excluding the top and bottom is approximately 2.77 square meters.
To calculate the area of one end of the roof (b), we need to find the area of a circular segment.
Given that the radius of the circle is 10 meters and the angle of the circle is 120 degrees, we can use the formula for the area of a circular segment:
Area = (θ/360) * π * r^2
where θ is the angle of the segment in degrees, and r is the radius of the circle.
Plugging in the values, we have:
Area = (120/360) * π * 10^2
= (1/3) * π * 100
= (1/3) * 3.14 * 100
≈ 104.67 square meters
So, the area of one end of the roof is approximately 104.67 square meters.
To calculate the area of the curved surface of the roof (c), we need to find the lateral surface area of a cone with a slant height of 20 meters.
The lateral surface area of a cone can be calculated using the formula:
Lateral Surface Area = π * r * l
where r is the radius of the base, and l is the slant height of the cone.
In this case, the radius of the base is 10 meters, and the slant height is 20 meters.
Plugging in the values, we have:
Lateral Surface Area = π * 10 * 20
= 200π
≈ 628.32 square meters
So, the area of the curved surface of the roof is approximately 628.32 square meters.
To calculate the cost of covering the two ends and the curved surface with galvanized iron, we need to calculate the total surface area of the roof.
Total Surface Area = 2 * Area of the end + Area of the curved surface
Plugging in the values we calculated earlier, we have:
Total Surface Area = 2 * 104.67 + 628.32
= 209.34 + 628.32
= 837.66 square meters
Now, we need to calculate the cost of covering this area with galvanized iron.
Cost = Total Surface Area * Cost per square meter
Plugging in the cost per square meter as £80, we have:
Cost = 837.66 * 80
≈ £66,932.80
So, the nearest cost of covering the two ends and the curved surface with galvanized iron would be around £66,932.80.