Question

The volume of a solid right circular cone is 11088 cm3.if it's height is 24 cm then find the radius of cone

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Radius \: of \: cone = 21 \: cm}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Volume \: of \: cone = 11088 \: {cm}^{3} \\ \\ \tt: \implies Height \: of \: cone = 24 \: cm \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Radius \: of \: cone =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Volume \: of \: cone = \frac{1}{3} \pi {r}^{2} h \\ \\ \tt: \implies 11088 = \frac{1}{3} \times \frac{22}{7} \times {r}^{2} \times 24 \\ \\ \tt: \implies 11088 \times 3 = \frac{22}{7} \times 24 \times {r}^{2} \\ \\ \tt: \implies \frac{11088 \times 3 \times 7}{22 \times 24} = {r}^{2} \\ \\ \tt: \implies 441 = {r}^{2} \\ \\ \tt: \implies r = \sqrt{441} \\ \\ \green{\tt: \implies r = 21 \: cm} \\ \\ \green{\tt \therefore Radius \: of \: cone \: is \: 21 \: cm}$

Answer 2

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{Length \ of \ radius \ is \ 21 \ cm}$

$\sf\orange{Given:}$

$\sf{\implies{Volume \ of \ cone=11088 \ cm^{3}}}$

$\sf{\implies{Height(h)=24 \ cm}}$

$\sf\pink{To \ find:}$

$\sf{Radius(r) \ of \ the \ cone.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Volume \ of \ cone=\frac{1}{3}\times \ \pi\times \ r^{2}\times \ h}$

$\sf{\implies{11088=\frac{1}{3}\times\frac{22}{7}\times \ r^{2}\times24}}$

$\sf{\implies{r^{2}=\frac{11088\times3\times7}{22\times24}}}$

$\sf{\implies{r^{2}=441}}$

$\sf{On \ taking \ square \ root \ of \ both \ sides}$

$\sf{r=21 \ cm}$

$\sf\purple{\tt{\therefore{Length \ of \ radius \ is \ 21 \ cm}}}$