Question

find the volume of the following solid figures using the steps provided.use π = 3.14. Express your answer to the nearest hundreds​

Answer 1

Answer :-

Volume of sphere = 904.32 cubic inches

Step-by-step explanation :-

Analyzing the question,

Given:

• Radius of sphere = 6 inches
• Value of π = 3.14

To find:

Volume of sphere = ?

Solution:

For finding the volume of sphere we use this formula:

$\blue{ \star} \: \: \pink{ \sf{Volume \: of \: sphere = \dfrac{4}{3} \pi {r}^{3} }}$

$\implies \sf{Volume = \dfrac{4}{3} \times 3.14 \times (6)^{3} }$

$\implies \sf{Volume = \dfrac{4}{3} \times 3.14 \times 216 }$

$\implies \sf{Volume = \dfrac{4}{ \cancel{3}} \times 3.14 \times \cancel{216} \: \: ^{72} }$

$\implies \sf{Volume = 4 \times 3.14 \times 72}$

$\implies \sf{Volume = 904.32 \: \: in {}^{3} }$

$\therefore \red{\boxed{\bf{Volume \: of \: sphere = 904.32 \: \: in^{3}}}}$

Answer 2

Answer:

$\begin{gathered}{\underline{\underline{\maltese{\large{\textsf{\textbf{ Given:}}}}}}}\end{gathered}$

• ★ Radius of Sphere = 6 inches

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\large{\textsf{\textbf{ To Find:}}}}}}}\end{gathered}$

• ★ Volume of Sphere

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\large{\textsf{\textbf{ Using Formula:}}}}}}}\end{gathered}$

$\begin{gathered}\dag{\underline{\boxed{\sf{ \sf{Volume \: of \: sphere = \dfrac{4}{3} \pi{r}^{3}}}}}}\end{gathered}$

Where

• ★ π = 3.14
• ★ r = radius

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\large{\textsf{\textbf{ Diagram:}}}}}}}\end{gathered}$

$\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bf 6in}\end{picture}$

• See this diagram from website Brainly.in.

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\large{\textsf{\textbf{ Solution:}}}}}}}\end{gathered}$

$\begin{gathered}\quad{:\implies{\sf{Volume \: of \: sphere = \bf\dfrac{4}{3} \pi{r}^{3}}}}\end{gathered}$

• Substituting the values

$\begin{gathered}\quad{:\implies{\sf{Volume \: of \: sphere = \bf\dfrac{4}{3} \times 3.14 \times {(6)}^{3}}}}\end{gathered}$

$\begin{gathered}\quad{:\implies{\sf{Volume \: of \: sphere = \bf\dfrac{4}{3} \times 3.14 \times {(6 \times 6 \times 6)}}}}\end{gathered}$

$\begin{gathered}\quad{:\implies{\sf{Volume \: of \: sphere = \bf\dfrac{4}{3} \times 3.14 \times {(216)}}}}\end{gathered}$

$\begin{gathered}\quad{:\implies{\sf{Volume \: of \: sphere = \bf\dfrac{4}{\cancel{3}}\times 3.14 \times {\cancel{216}}}}}\end{gathered}$

$\begin{gathered}\quad{:\implies{\sf{Volume \: of \: sphere = \bf{4}\times 3.14 \times 72}}}\end{gathered}$

$\begin{gathered}\quad{:\implies{\sf{Volume \: of \: sphere = \bf{904.32 \: {in}^{3} }}}}\end{gathered}$

$\begin{gathered}\quad\dag{\underline{\boxed{\sf{\purple{Volume \: of \: sphere ={904.32 \: {inches}^{3}}}}}}}\end{gathered}$

• Henceforth,The Volume of Sphere is 904.32 inches³.

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\large{\textsf{\textbf{ Additional Information :}}}}}}}\end{gathered}$

Formulas related to SA & Volume :

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