Question

A large planetarium in the shape of a dome is being built at MHS. When it is complete, the base of the dome will have a circumference of 870 meters. What is the area of land required for this planetarium

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Area\:required\:for\:planetarium=60145.3184\:m^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies Circumference \: of \: dome = 870 \: m \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Area \:required \:for \: planetarium= ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Circumference \: of \: dome = 870 \: m \\ \\ \tt: \implies 2\pi r = 870 \\ \\ \tt: \implies r = \frac{870}{2\pi} \\ \\ \tt: \implies r = \frac{870 \times 7}{2 \times 22} \\ \\ \green{\tt: \implies r = 138.4 \: m} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: planetarium = \pi {r}^{2} \\ \\ \tt: \implies Area \: of \: planetarium = 3.14 \times {138.4}^{2} \\ \\ \tt: \implies Area \: of \: planetarium=3.14 \times 19154.56 \\ \\ \green{\tt: \implies Area \: of \: planetarium =60145.3184 {m}^{2} }$

Answer 2

Answer:

☆ ANSWER ☆

GIVEN :

CIRCUMFERENCE OF THE DOME = 870 M

TO FIND :

AREA REQUIRED BY THE DOME

PROOF :

$circumerence = 2r\pi \\ 870 = 44 \div 7 \times r \\ r = 138.40$

THEREFORE ;

$area \: = \pi {r}^{2} \\ = 3.14 \times 138.4 {}^{2} \\ = 3.14 \times 19154.56 \\ = 60145.318 \: m$

HOPE THAT HELPS