Respuesta :
Answer:
1. The amount of ice needed for the sculpture is 18 m³
2. The amount of fabric needed to manufacture the umbrella is 0.757 m²
3. The height of the cone is 37.5 cm
4. The largest possible storage area which is obtained by attaching the storage area to the back of the building is 87.11 m²
Step-by-step explanation:
1. The volume, V, of a rectangular pyramid = [tex]\dfrac{1}{3} \cdot B \cdot h[/tex]
Where:
B = Base area = Length, L × Width, W
h = Height of the pyramid = 3.6 m
L = 5 m
W = 3 m
The volume = 1/3 × 5 × 3 × 3.6 = 18 m³
The amount of ice needed for the sculpture is 18 m³
2) The surface area of a cone = π·r·s
s = Slant height
r = Radius of the cone's base = 0.4 m
h = The height of the cone = 0.45m
s = √(0.4² + 0.45²) = (√145)/20
The surface area of the cone = π × 0.4 × (√145)/20 = 0.757 m²
The amount of fabric needed to manufacture the umbrella is 0.757 m²
3) The volume, V of the cone = 150 cm³
The base area, [tex]A_b[/tex], of the cone = 12 cm²
The height of the cone = h
We note that the volume of a cone = [tex]\dfrac{1}{3} \cdot A_b \cdot h[/tex]
Therefore;
[tex]\dfrac{1}{3} \times 12 \times h = 150[/tex]
4·h = 150
h = 150/4 = 37.5 cm
The height of the cone = 37.5 cm
4) The storage area at the back corner with four sides = 100 m²
The storage area at the back of the building with three sides = 98 m²
Given that the available riling = 28 m, we have;
For maximum area the four sides should be equal, hence dimension of each side = 28/4 = 7
The area of storage space that can be fenced on four sides at the back corner = 7 × 7 = 49 m²
At the back of the building only three sides need fencing, we therefore have;
The side length = 28/3 = [tex]9\frac{1}{3}[/tex]
The area fenced = [tex]\left 9\frac{1}{3} \right \times 9\frac{1}{3} = 87\frac{1}{9} \ m^2[/tex] = 87.11 m²
Therefore, the largest possible storage area, 87.11 m², is obtained by attaching the storage area to the back of the building.
