Question

Please help i don't feel ok

Question 1(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)

Bradenton Bakery is baking a cake for a customer's quinceañera. The cake mold is shaped like a cylinder with a diameter of 8 inches and height of 6 inches.

Which of the following shows a correct method to calculate the number of cubic units of cake batter needed to fill the mold? Approximate using pi equals 355 over 113.

V equals 355 over 113 times 8 squared times 6
V equals 355 over 113 times 6 squared times 8
V equals 355 over 113 times 6 squared times 4
V equals 355 over 113 times 4 squared times 6
Question 2(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)

What is the volume of a right circular cylinder with a diameter of 10 meters and a height of 16 meters. Leave the answer in terms of π.

400π m3
1,600π m3
160π m3
1,256π m3
Question 3(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)

What is the volume of the cylinder? Round to the nearest hundredth and approximate using π = 3.14.

cylinder with a segment from one point on the circular base to another point on the base through the center labeled 3.2 feet and a height labeled 3.8 feet

122.18 cubic feet
76.36 cubic feet
38.18 cubic feet
30.55 cubic feet
Question 4(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)

A helium tank shaped like a cylinder has 4,096π in3 of space inside the tank. If the diameter of the helium tank is 16 inches, what is its height?

16 inches
8 inches
64 inches
32 inches
Question 5(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)

A soccer player has a large cylindrical water cooler that measures 3 feet in diameter and is 4 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth.

28.26 gallons
113.04 gallons
211.38 gallons
845.54 gallons
Question 6(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)

Coins are placed into a treasure chest, and each coin has a radius of 1.2 inches and a height of 0.0625 inches. If there are 250 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π = 3.14.

0.28 in3
70.65 in3
117.75 in3
282.60 in3
Question 7(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)

A cylinder has a volume of 1 and one third in3 and a radius of one third in. What is the height of a cylinder? Approximate using pi equals 22 over 7.

42 over 6 inches
42 over 9 inches
42 over 11 inches
42 over 22 inches

Answer 1

Question 1 : V equals 355 over 113 times 4 squared times 6

Question 2: 400π m3

Question 3: 30.55 cubic feet

Question 4: 64 inches

Question 5: 211.38 gallons

Question 6: 70.65 in³

Question 7: 42 over 11 inches

Explanation:

For all four questions, the formula used for the volume of a cylinder is
V = πr²h

where r = radius of the cylinder = diameter / 2

h = height

Question 1

The radius of the cake is diameter/2 = 8/2 = 4 in

The height of the cake = 5 in

Therefore the volume of batter required is

V = π x 4² x 6

With π = 355113 that works out to
V = 355/133 x 4² x 6

This corresponds to the last choice given as:
V equals 355 over 113 times 4 squared times 6

Question 2

Given diameter = 10, r = 10/2 = 5 meters
h = 16 meters

V = π x 5² x 16

V = π x 25 x 16

V = π x 400

V = 400π m³

This corresponds to the first choice

Question 3

The phrase "...segment from one point on the circular base to another point on the base through the center.."

is nothing but a convoluted expression for the diameter!

So diameter = 8.2 feet
radius r = 3.2 / 2 = 1.6 feet

h = 3.8 feet

π = 3.14

V = πr²h

V = 3.14 x (1.6)² x 3.8

= 3.14 x 2.56 x 3.8

= 30.54592

= 3.55 cubic feet rounded to nearest hundredth

This is the fourth (and last) option

Question 4

Volume is given as 4096π in³

r = 16/2 = 8 inches

r² = 8² = 64

Since V = πr²h,

h = V/πr²

= 4096π/64π

= 64 inches

Option 3

Question 5

r = 3/2 = 1.5 feet

h = 4 feet

π = 3.14

V =3.14 x (1.5)² x 4

= 28.26 cubic feet

Since 1 cubic foot = 7.48 gallons,

28.26 cubic feet = 28.26 x 7.48 = 211.3848 = 211.38 gallons (rounded)
This the third option

Question 6

Volume of each coin = 3.14 x 1.2² x 0.0625 = 2.826 cubic inches

For 250 coins, the total volume = 2.826 x 250 = 70.65 in³

Question 7

V = 1 1/3 in³ = 4/3 in³

r = 1/3 in

π =22/7

V = πr²h

h = V/πr²

r² = 1/3 x 1/3 = 1/9

πr² = 22/7 x 1/9 = 22/63

h = V/πr² = 4/3 ÷ 22/63 = 4/3 x 63/22 = 252/66
= 42/11 (by dividing numerator and denominator by 6)

= 42 over 11 (third choice)