24.08.2020

The cone shaped roof has the height of 30ft and the radius of 15ft find it's lateral area and the surface area

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09.07.2023, solved by verified expert
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Lateral surface area of cone is 1580 feet²Surface area of cone is 2287 feet²

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

Step-by-step explanation:

Given that Height of cone shaped roof is 30 ft and radius is 15 ft.

To calculate the lateral surface area and Surface area of the cone we will use the formula given below:

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

Finding the Slant height of the cone:

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

Hence, Slant height of cone is 33.54 feet.

Substituting values in above formula:

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

Hence, Lateral surface area of cone is 1580 feet²

Now, Calculating surface area:

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

The cone shaped roof has the height of 30ft and, №18010973, 24.08.2020 12:25

Hence, surface area of cone is 2287 feet²
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Mathematics
Step-by-step answer
P Answered by Specialist
Lateral surface area of cone is 1580 feet²Surface area of cone is 2287 feet²

\\

Step-by-step explanation:

Given that Height of cone shaped roof is 30 ft and radius is 15 ft.

To calculate the lateral surface area and Surface area of the cone we will use the formula given below:

\\

\star \: { \underline   { \boxed { \purple{ \pmb { \sf{Lateral \: surface \: Area  _{(cone)}  =  \pi rl}}}}}}

\\

\star{\underline{ \boxed{ \purple{ \pmb { \sf{Surface \: area _{(cone)} =  \pi rl +  \pi {r}^{2} }}}}}}

\\

Finding the Slant height of the cone:

\dashrightarrow \:  \:L =  \sqrt{ {(r)}^{2} +  {(h)}^{2}  }  \\

\dashrightarrow \:  \: L =  \sqrt{225 +900 }   \\

\dashrightarrow \:  \: L =  \sqrt{1125 }  \\

{   \dashrightarrow \:  \: { \pink{ \boxed { \: L  =   33.541 }}}}\\

Hence, Slant height of cone is 33.54 feet.

Substituting values in above formula:

\dashrightarrow \:  \: LSA =  \pi rl \\

\dashrightarrow \:  \: LSA =  \dfrac{22}{7}  \times 15 \times 33.54 \\

\dashrightarrow \:  \: LSA =  \dfrac{22 \times 15 \times 33054}{7}  \\

\dashrightarrow \:  \: LSA =  \dfrac{11068.2}{7}  \\

\dashrightarrow \:  \:{ \boxed { \pmb{ \sf {\pink{ LSA \:  \approx1580 \:  {ft}^{2}}}} }} \\

\\

Hence, Lateral surface area of cone is 1580 feet²

Now, Calculating surface area:

\dashrightarrow \:  \:SA =  \pi rl +  \pi {r}^{2}  \\

\dashrightarrow \:  \:SA = \pi (15)(33.54) + \pi {(15)}^{2}  \\

\dashrightarrow \:  \:SA = \pi(503.1) +  22 5 \pi \\

\dashrightarrow \:  \: SA = 728.1 \pi \\

\dashrightarrow \:  \:SA = 728.1  \times 3.14 \\

\dashrightarrow \:  \:{ \boxed{ \pmb{ \pink{ \sf{SA \approx2287 \:  {ft}^{2} }}}}}

\\

Hence, surface area of cone is 2287 feet²
Mathematics
Step-by-step answer
P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics
Step-by-step answer
P Answered by PhD
Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram
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 

Mathematics
Step-by-step answer
P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Mathematics
Step-by-step answer
P Answered by PhD

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

Mathematics
Step-by-step answer
P Answered by PhD
The answer is in the image 

The answer is in the image 

Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 

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