07.01.2022

a. complete the table by giving the radius, diameter and area of each circle.

. 4

Faq

Mathematics
Step-by-step answer
P Answered by PhD

Ques 1)

CAN D

Ques 2)

252 pi in.^2

Ques 3)

288 pi cm^3

Ques 4)

2080 pi ft. ^2

Ques 5)

540 pi in. ^3

Step-by-step explanation:

Let r denote the radius of the cylinder.

and h denote the height of the cylinder.

Ques 1)

We know that the least amount of paper is required by the can whose lateral surface area is the smallest.

We know that the lateral surface area of cylinder is given by:

LA=2\pi rh

CAN               Radius             Height              Lateral Area

 A                   2 in.                 6 in.              75.36 square in.

 B                   2.5 in.              5 in.              78.5 square in.

 C                   3 in.                  4 in.               75.36 square in.  

 D                   3.2 in.               3 in.               60.288 square in.

Hence, the can that requires the least amount of paper is:

CAN D.

Ques 2)

r=6 in.

h=15 in.

The surface area of cylinder is calculated as:

SA=2\pi r^2+2\pi rh

Hence, on putting the given values in the formula we have:

SA=2\pi\times 6^2+2\pi \times 6\times 15\\\\SA=252\pi\ in.^2

Hence,

SA=252 pi in.^2.

Ques 3)

diameter(d)=8 cm.

This means that:

r=d/2=4 cm.

h=18 cm.

Hence, the volume(V) of the cylinder is calculated as:

V=\pi r^2h\\\\V=\pi\times (4)^2\times 18\\\\V=288\pi\ cm^3

Hence,

Volume is: 288 pi cm^3

Ques 4)

d=40 feet.

h=32 feet.

Hence, r=d/2=40/2=20 feet.

Hence, the surface area of the cylinder is calculated as:

SA=2\pi r^2+2\pi rh\\\\SA=2\pi\times (20)^2+2\pi\times  20\times 32\\\\SA=2080\pi\ ft.^2

Hence, SA=2080 pi ft. ^2

Ques 5)

r=6 in.

h=15 in.

Hence, the volume of the cylinder is given by:

V=\pi r^2h\\\\V=\pi \times (6)^2\times 15\\\\V=540\pi\ in.^3

Hence,

Volume= 540 pi in. ^3

Mathematics
Step-by-step answer
P Answered by PhD

Ques 1)

CAN D

Ques 2)

252 pi in.^2

Ques 3)

288 pi cm^3

Ques 4)

2080 pi ft. ^2

Ques 5)

540 pi in. ^3

Step-by-step explanation:

Let r denote the radius of the cylinder.

and h denote the height of the cylinder.

Ques 1)

We know that the least amount of paper is required by the can whose lateral surface area is the smallest.

We know that the lateral surface area of cylinder is given by:

LA=2\pi rh

CAN               Radius             Height              Lateral Area

 A                   2 in.                 6 in.              75.36 square in.

 B                   2.5 in.              5 in.              78.5 square in.

 C                   3 in.                  4 in.               75.36 square in.  

 D                   3.2 in.               3 in.               60.288 square in.

Hence, the can that requires the least amount of paper is:

CAN D.

Ques 2)

r=6 in.

h=15 in.

The surface area of cylinder is calculated as:

SA=2\pi r^2+2\pi rh

Hence, on putting the given values in the formula we have:

SA=2\pi\times 6^2+2\pi \times 6\times 15\\\\SA=252\pi\ in.^2

Hence,

SA=252 pi in.^2.

Ques 3)

diameter(d)=8 cm.

This means that:

r=d/2=4 cm.

h=18 cm.

Hence, the volume(V) of the cylinder is calculated as:

V=\pi r^2h\\\\V=\pi\times (4)^2\times 18\\\\V=288\pi\ cm^3

Hence,

Volume is: 288 pi cm^3

Ques 4)

d=40 feet.

h=32 feet.

Hence, r=d/2=40/2=20 feet.

Hence, the surface area of the cylinder is calculated as:

SA=2\pi r^2+2\pi rh\\\\SA=2\pi\times (20)^2+2\pi\times  20\times 32\\\\SA=2080\pi\ ft.^2

Hence, SA=2080 pi ft. ^2

Ques 5)

r=6 in.

h=15 in.

Hence, the volume of the cylinder is given by:

V=\pi r^2h\\\\V=\pi \times (6)^2\times 15\\\\V=540\pi\ in.^3

Hence,

Volume= 540 pi in. ^3

Mathematics
Step-by-step answer
P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

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