Question

what is the diameter of a hemispherical dome if it's volume is 200m^3​

Answer 1

$\large \color{red} \bold{Given,} \\ \\ \sf \: Volume \: of \: cone \: = \: 200 \: {m}^{3} \\ \\ \color{aqua} \bold{To \: find \: the \: Diameter} \\ \\ \color{gold} \bold{Solution \: ―} \\ \\ \sf \: Volume_{(hemisphere)} \: = \: \frac{2}{3} \: \pi {r}^{3} \\ \\ \sf \: 200 \: = \: \frac{2}{3} \: \times \: \frac{22}{7} \: \times \: {r}^{3} \\ \\ \sf \:200 \: = \: 2.09 \: {r}^{3} \\ \\ \sf \: {r}^{3} \: = \: \frac{200}{2.09} \\ \\ \sf \: {r}^{3} \: = \: 97.69 \\ \\ \sf \: r \: = \: \sqrt[3]{97.69} \\ \\ \sf \color{silver} \: Radius \: = \: 4.6 \: m \: \: \{approx \} \\ \\ \sf \: Diameter \: = \: 2 \: \times \: Radius \\ \\ \sf \: Diameter \: = \:2 \: \times \: 4.6 \\ \\ \sf \: \color{magenta}Diameter \: = \:9.2 \: m$

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$\color{green} \large\bold{Extra \: formulas}$

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²