Can you quickly solve this? and all of the questions

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

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