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

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

The solution is given in the image below

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

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

Mathematics
Step-by-step answer
P Answered by PhD

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

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