Question

volume and surface area of solid hemispehere are numerically equal . what is the diameter of hemispehere​

Answer 1

Answer:

answer is 9 cm

Step-by-step explanation:

3πr^2=2/3πr^3

3=2/3r

r=9/2cm

diameter =2r

diameter=2*9/2

diameter=9cm

Answer 2

$\sf\orange{ \underline{Question:-}}$

Volume and surface area of solid hemispehere are numerically equal . what is the diameter of hemispehere.

$\sf\orange{ \underline{Required\:Answer:-}}$

The diameter of hemisphere is 9 units.

$\sf\underline\pink{Given:-}$

• Volume and Surface area of solid hemisphere are numerically equal.

$\sf\underline\blue{To\:Find:-}$

• Diameter of hemisphere

$\sf\underline\red{Solution:-}$

Volume of hemisphere = $\sf \dfrac{2}{3} \pi r^3$

Surface area of hemisphere = $\sf 3\pi r^2$

=> $\sf 3\pi r^2 = \dfrac{2}{3} \pi r^3$

=> $\sf r = \dfrac{9}{2}$

=> $\sf 2r = 9$

=> $\sf D = 9$

Therefore, Diameter of hemisphere (D) = 9 units.

Additional Information:-

formulas related to SA and volume

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

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