Question

please answer it....​

Answer 1

Florence wants to invest money abroad. Florence is aware that France generally has a recession every 6 years and America generally has a recession every 8. in the year 2005, both France and America were in recession. Florence needs to work out the next time they will both be in recession. When will this be?

Answer 2

Answer:

Diαgrαm :

$\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf{7\ cm}}\put(9.5,10){\sf{24\ cm}}\end{picture}$

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

Given :

• → Volume of cone = 1212 cm³.
• → Height of cone = 24 cm.

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

To Find :

• → Radius of cone
• → Slant height of cone
• → Surface area of cone

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

Using Formυlαs :

$\small\longrightarrow{\underline{\boxed{\pmb{\sf{Volume \: of \: cone = \dfrac{1}{3}\pi{r}^{2}h}}}}}$

$\small\longrightarrow{\underline{\boxed{\pmb{\sf{l= \sqrt{{r}^{2} + {h}^{2}}}}}}}$

$\small\longrightarrow{\underline{\boxed{\pmb{\sf{S.A \: of \: cone = \pi{rl}}}}}}$

Where :-

• r = radius
• h = height
• l = slant height
• SA = surface area

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

Solυtion :

$\small\bigstar$ Firstly, finding the radius of cone by substituting the values in the formula :-

$\begin{gathered}\qquad\longrightarrow{\bf{Volume \: of \: cone = \dfrac{1}{3}\pi{r}^{2}h}} \\ \\ \quad\longrightarrow{\sf{1212 = \dfrac{1}{3} \times \frac{22}{7} \times {r}^{2} \times 24}} \\ \\ \qquad\longrightarrow{\sf{1212 = \dfrac{1 \times 22}{3 \times 7}\times {r}^{2} \times 24}} \\ \\ \qquad\longrightarrow{\sf{1212 = \dfrac{22}{21}\times {r}^{2} \times 24}} \\ \\ \quad\longrightarrow{\sf{\dfrac{1212}{24} = \dfrac{22}{21}\times {r}^{2}}} \\ \\ \quad\longrightarrow{\sf{\cancel{\dfrac{1212}{24}}= \dfrac{22}{21}\times {r}^{2}}} \\ \\ \quad\longrightarrow{\sf{50.5 = \dfrac{22}{21}\times {r}^{2}}} \\ \\ \quad\longrightarrow{\sf{{r}^{2} = 50.5 \times \dfrac{21}{22}}} \\ \\ \quad\longrightarrow{\sf{{r}^{2} = \dfrac{50.5 \times 21}{22}}} \\ \\ \quad\longrightarrow{\sf{{r}^{2} = \dfrac{50.5 \times 21}{22}}} \\\end{gathered}$

$\begin{gathered}\quad\qquad\qquad\longrightarrow{\sf{{r}^{2} = \dfrac{1060.5}{22}}} \\ \\ \quad\qquad\qquad\longrightarrow{\sf{{r}^{2} = \cancel{\dfrac{1060.5}{22}}}} \\ \\ \quad\quad\qquad\longrightarrow{\sf{{r}^{2} \approx 48.20 }}\\ \\ \quad\qquad\qquad\longrightarrow{\sf{r \approx \sqrt{48.20}}} \\ \\ \qquad\qquad\longrightarrow{\sf{r \approx 7 \: cm}} \\ \\ \qquad\qquad\bigstar{\underline{\boxed{\sf{\pink{Radius \approx 7 \: cm}}}}}\end{gathered}$

∴ The radius of cone is 7 cm.

$\rule{300}{1.5}$

$\small\bigstar$ Now, finding the slant height of cone by substituting the values in the formula :-

$\begin{gathered} \qquad{\longrightarrow{\bf{l= \sqrt{{r}^{2} + {h}^{2}}}}} \\ \\ \qquad{\longrightarrow{\sf{l= \sqrt{{(7)}^{2} + {(24)}^{2}}}}} \\ \\ \qquad{\longrightarrow{\sf{l= \sqrt{(7 \times 7)+ (24 \times 24)}}}} \\ \\ \quad{\longrightarrow{\sf{l= \sqrt{49+ 576}}}} \\ \\ \quad{\longrightarrow{\sf{l= \sqrt{625}}}} \\ \\ \quad{\longrightarrow{\sf{l= \sqrt{25 \times 25}}}} \\ \\ \quad{\longrightarrow{\sf{l= 25 \: cm}}} \\ \\ \quad\bigstar{\underline{\boxed{\sf{\pink{Slant \: height = 25 \: cm}}}}}\end{gathered}$

∴ The slant height of cone is 25 cm.

$\rule{300}{1.5}$

$\small\bigstar$ Now, finding the surface area of cone by substituting the values in formula :-

$\begin{gathered} \qquad{\longrightarrow{\bf{Surface \: area\: of \: cone = \pi{rl}}}} \\ \\ \qquad{\longrightarrow{\sf{Surface \: area= \frac{22}{7} \times 7 \times 25 }}} \\ \\ \qquad{\longrightarrow{\sf{Surface \: area= \frac{22}{\cancel{7}} \times \cancel{7} \times 25 }}} \\ \\ \quad{\longrightarrow{\sf{Surface \: area= 22\times 25}}} \\ \\ \qquad{\longrightarrow{\sf{Surface \: area = 550 \: {cm}^{2}}}} \\ \\ \bigstar\underline{\boxed{\sf{\pink{Surface \: area = 550 \: {cm}^{2}}}}}\end{gathered}$

∴ The surface area of cone is 550 cm².

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

Leαrn More :

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

$\rule{300}{1.5}$