Question

Find the radius of a sphere whose surface area is 154cm².​with stepss

Answer 1

Answer:

THIS IS YOUR ANSWER:

$area \: of \: spere \: = 4\pi \: r {}^{2} \\ 154cm {}^{2} = 4 \times \frac{22}{7} \times r {}^{2}$

$\frac{154 \times 7}{4 \times 22} = r {}^{2} \\ r {}^{2} = 12.25$

$r = \sqrt{12.25} \\ r = 3.5cm$

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Answer 2

Answer:

The radius of sphere is 3.5 cm.

Step-by-step explanation:

SOLUTION :

Here's the required formula to find the radius of sphere :

$\longrightarrow{\pmb{\sf{SA_{(Sphere)} = 4 \pi{r}^{2}}}}$

• → SA = surface area
• → π = 22/7
• → r = radius

Substituting all the given values in the formula to find the radius of sphere :

$\longrightarrow{\sf{SA_{(Sphere)} = 4 \pi{r}^{2}}}$

$\longrightarrow{\sf{154 = 4 \times \dfrac{22}{7} \times {r}^{2}}}$

$\longrightarrow{\sf{154 = \dfrac{88}{7} \times {r}^{2}}}$

$\longrightarrow{\sf{{r}^{2} = 154 \times \dfrac{7}{88} }}$

$\longrightarrow{\sf{{r}^{2} = \dfrac{1078}{88} }}$

$\longrightarrow{\sf{{r}^{2} = 12.25}}$

$\longrightarrow{\sf{r = \sqrt{12.25}}}$

$\longrightarrow{\sf{r = 3.5}}$

$\star{\boxed{\sf{\pmb{r = 3.5 \: cm}}}}$

Hence, the radius of sphere is 3.5 cm.

$\rule{200}2$

DIAGRAM :

Here's the diagram of sphere with radius 3.5 cm.

$\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bf{3.5\ cm}}\end{picture}$

$\rule{300}{2.5}$