Show the steps taken to complete the problems:

volume of a cylinder: 34m diameter and 27m height
use 3.14 for pi.

find the surface area of the cone. 8in. diameter and 7in. height.

find the lateral area of the square pyramid: 8in. base and 22in. slant

Volume cylinder = 24501.42 m³

The surface area of the cone = 151.5 in²

The lateral area of the square pyramid = 352 in²

Step-by-step explanation:

∵ The volume of the cylinder = area base × height

∵ Its base is a circle

∴ V = πr² × h = 3.14 × (34/2)² × 27 = 24501.42 m³

∵ The surface area of the cone = 1/2 perimeter base ×  Slant height + area base

∵ Its base is a circle

∴ S.A = (1/2) × 2πr × l + πr²

∵ The slant height =

∴ S.A = 3.14 × (8/2) × √65 + 3.14 × (8/2)² = 151.5 in²

∵ The lateral area of the square pyramid = 1/2 perimeter base × slant height

∵ Its base is a square

∴ L.A = 1/2 × (8 × 4) × 22 = 352 in²

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.