Question 10.2.5
Lateral Area is given by
L =2*pi*r*h = 2*3.14*(18yd/2)*14yd = 791,3 yd²
Total Area is given by
At = L + 2*Area of lid = L + 2*[pi*r(**2)] = 791,3 yd² + 2*[3.14*(9yd)**2]
At = 791,3 yd² + 508.7 yd² = 1300yd²
Question 10.2.6
Lateral Area is given by
L =2*pi*r*h = 2*3.14*7ft*9ft = 395.6 ft²
Total Area is given by
At = L + 2*Area of lid = L + 2*[pi*r(**2)] = 395.6 ft² + 2*[3.14*(7ft)²]
At = 395.6 ft² + 307.7 ft² = 703.3 ft²
Question 10.2.7
Finding surface Area lets you calculate the dimensions of a certain product.
By knowing this you can estimate how many products can fit a certain container, how many you can stack together (Assuming you can calculate its volume too).
Also by knowing the function of the Area you can apply calculus to minimize or maximize the results in certain conditions, which is beneficial in terms of packaging.
Question 6-Second picture
Lets calculate the volume of the cylinder, which is
Vc = pi*r²*h = 3.14*(1.6cm)² * 6.2 cm = 49.8 cm³
Volume of the Half Sphere
Vhs = 1/2 * [4/3*pi*r³] = 0.5*[4/3*3.14*(1.6cm)³] = 8.6 cm³
Volume of the whole container = 49.8 cm³ + 8.6 cm³ = 58.4 cm³
Question 9.1.1 (Third picture)
Volume of the cylinder = pi*r²*h = 3.14*(6ft)² * 8ft = 904.3 ft³
Question 9.1.2
The can can be represented like a cylinder
Volume of the cylinder = pi*r²*h = 3.14*(4in)² * 7 in = 351.7 in³
Question 9.2.3 (Cones)
The volume of a cone is given by
Vcone = 1/3 * [Volume cylinder] = 1/3 *[3.14 * r² *h]
V cone = 1/3 *[ 3.14*(6cm)² *15cm ] = 565.2 cm³
Question 9.2.4
Vcone = 1/3 * [Volume cylinder] = 1/3 *[3.14 * r² *h]
V cone = 1/3 *[ 3.14*(12in)² *20in ] = 3014.4 in³
Question 9.3.5 (Spheres)
Volume Sphere = [4/3*pi*r³]
Vs = 4/3*3.14 * (3ft)³ = 113.0 ft³
Question 9.3.6 (Spheres)
Volume Sphere = [4/3*pi*r³]
Vs = 4/3*3.14 * (13/2cm)³ = 1149.8 cm³