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kris22elizondop9v1bb

05.04.2022 •

Mathematics

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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Ответ:

sweetgigi2364

05.04.2022

Lateral surface area of cone is 1580 feet²Surface area of cone is 2287 feet²

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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

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Ответ:

Jerrygordon212

28.05.2022

Yes SAS

Step-by-step explanation:

There are two sides congruent and one angle congruent

0,0(0 оценок)

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