[tex]__________________________[/tex]
First, let us find the radius
[tex]\sf \large R = \frac{diameter}{2} [/tex]
[tex]\sf \large R = \frac{15 \: m}{2} [/tex]
[tex]\sf \large R = 7.5 \: m[/tex]
Second, find the surface area
[tex]\sf \large SA = 4 \pi r^{2} [/tex]
[tex]\sf \large SA = (4)(3.14)(7.5)^{2} [/tex]
[tex]\sf \large SA = (4)(3.14)(56.25)[/tex]
[tex]\sf \large SA = (12.56)(56.25)[/tex]
[tex]\sf \large SA = \boxed{ \sf 707 \: m^{2} }[/tex]
↬ Hence, the surface area of the sphere is 707 m^2
Before finding surface area of circle , we have to convert diameter to radius.
[tex] \\ \\ [/tex]
Formula :
[tex] \boxed{ \pmb{ \rm Radius = \frac{diameter}{2} }}[/tex]
Steps :-
[tex] \dashrightarrow\sf Radius = \dfrac{diameter}{2}[/tex]
[tex] \dashrightarrow\sf Radius = \dfrac{15}{2}[/tex]
[tex] \dashrightarrow\sf Radius = 7.5[/tex]
Digram :
[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{ 7.5 \: m}}\end{picture}[/tex]
Now we know :
[tex] \boxed{ \pmb{ \rm{surface \: area_{(sphere)} = 4\pi {r}^{2} }}}[/tex]
Steps :
[tex] \small \dashrightarrow \sf{surface \: area_{(sphere)} = 4\pi {r}^{2} }[/tex]
[tex] \\ [/tex]
[tex] \small \dashrightarrow \sf surface \: area_{(sphere)} = 4 \times \dfrac{22}{7} \times 7.5 \times 7.5 \\ [/tex]
[tex] \small \dashrightarrow \sf surface \: area_{(sphere)} = 4 \times \dfrac{22}{7} \times 56.25 \\ [/tex]
[tex] \small \dashrightarrow \sf surface \: area_{(sphere)} =\dfrac{88}{7} \times56.5 \\ [/tex]
[tex] \small \dashrightarrow \sf surface \: area_{(sphere)} =\dfrac{4950}{7} \\ [/tex]
[tex] \purple{\dashrightarrow \frak{ \pmb{surface \: area_{(sphere)} =707.14 \{approx\}}}}\\ [/tex]
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Answers & Comments
SURFACE AREA
[tex]__________________________[/tex]
Given:
Answer & Solution:
First, let us find the radius
[tex]\sf \large R = \frac{diameter}{2} [/tex]
[tex]\sf \large R = \frac{15 \: m}{2} [/tex]
[tex]\sf \large R = 7.5 \: m[/tex]
Second, find the surface area
[tex]\sf \large SA = 4 \pi r^{2} [/tex]
[tex]\sf \large SA = (4)(3.14)(7.5)^{2} [/tex]
[tex]\sf \large SA = (4)(3.14)(56.25)[/tex]
[tex]\sf \large SA = (12.56)(56.25)[/tex]
[tex]\sf \large SA = \boxed{ \sf 707 \: m^{2} }[/tex]
↬ Hence, the surface area of the sphere is 707 m^2
Before finding surface area of circle , we have to convert diameter to radius.
[tex] \\ \\ [/tex]
Formula :
[tex] \boxed{ \pmb{ \rm Radius = \frac{diameter}{2} }}[/tex]
Steps :-
[tex] \dashrightarrow\sf Radius = \dfrac{diameter}{2}[/tex]
[tex] \dashrightarrow\sf Radius = \dfrac{15}{2}[/tex]
[tex] \dashrightarrow\sf Radius = 7.5[/tex]
[tex] \\ \\ [/tex]
Digram :
[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{ 7.5 \: m}}\end{picture}[/tex]
[tex] \\ \\ [/tex]
Now we know :
[tex] \boxed{ \pmb{ \rm{surface \: area_{(sphere)} = 4\pi {r}^{2} }}}[/tex]
[tex] \\ \\ [/tex]
Steps :
[tex] \small \dashrightarrow \sf{surface \: area_{(sphere)} = 4\pi {r}^{2} }[/tex]
[tex] \\ [/tex]
[tex] \small \dashrightarrow \sf surface \: area_{(sphere)} = 4 \times \dfrac{22}{7} \times 7.5 \times 7.5 \\ [/tex]
[tex] \\ [/tex]
[tex] \small \dashrightarrow \sf surface \: area_{(sphere)} = 4 \times \dfrac{22}{7} \times 56.25 \\ [/tex]
[tex] \\ [/tex]
[tex] \small \dashrightarrow \sf surface \: area_{(sphere)} =\dfrac{88}{7} \times56.5 \\ [/tex]
[tex] \\ [/tex]
[tex] \small \dashrightarrow \sf surface \: area_{(sphere)} =\dfrac{4950}{7} \\ [/tex]
[tex] \\ [/tex]
[tex] \purple{\dashrightarrow \frak{ \pmb{surface \: area_{(sphere)} =707.14 \{approx\}}}}\\ [/tex]
[tex] \\ \\ [/tex]