Question

in a right circular cone the hieght is 3times the radius of Base if volume is 134.75cm² then find the area of base​

Answer 1

Correct Question :

In a right circular cone the height is 3 times the radius of Base. If volume is 134.75 cm³, then find the area of base.

Solution :

Let the radius of base of the cone be r cm

Height of the cone h = 3 times the radius = 3r cm

Volume of the cone = 134.75 cm³

$\implies \dfrac{1}{3}\pi {r}^{2} h = 134.75$

$\implies \pi {r}^{2} h =404.25$

$\implies \dfrac{22}{7} \times {r}^{2} \times 3r =404.25$

$\implies \dfrac{66}{7} {r}^{3} =404.25$

$\implies {r}^{3} =404.25 \times \dfrac{6}{22}$

$\implies {r}^{3} =42.875$

$\implies {r}^{3} = \bigg(\dfrac{35}{10} \bigg)^{3}$

$\implies r = \dfrac{35}{10} = 3.5$

Area of the base of cone = Area of the circle

= πr²

$= \dfrac{22}{7} \times {3.5}^{2}$

$= \dfrac{22}{7} \times 3.5 \times 3.5$

= 22 * 3.5 * 0.5

= 11 * 3.5

= 38.5

i.e Area of the base = 38.5 cm²

Hence, area of the base is 38.5 cm².

Answer 2

Question :-

In a right circular cone the hieght is 3times the radius of Base if volume is 134.75cm² then find the area of base..?

Answer :-

→ Area of base of this cone is 38.5 cm²

To Find :-

→Area of base of circular cone .

Formula used:-

$\star \: \: \sf{ \red{volume \: of \: cone(v)} = \orange{ \frac{1}{3} \pi \: {r}^{2} \: h}} \\ \\ \star \sf{ \: \red{area} \: of \: \green{base} \: of \: \orange{circular} \: cone} = \sf{ \pi \: {r}^{2} }$

Step - by - step explanation :-

Given that ,

• Volume of cone ( v ) = 134.75 cm²
• Height (h) = 3 × r

Solution :-

• Volume of cone (v) = 134.75 cm²

apply the given formula ,

$\rightarrow \sf{ \red{\frac{1}{3}} \pi \: \green{ {r}^{2} \: h }\: = \orange{134.75}} \\ \\ \because \sf{ \red{h \: = 3 \: r}} \\ \therefore \: \\ \rightarrow \sf{ \blue{\frac{1}{3} \times \frac{22}{7} }\red{ \times 3 {r}^{3}} = 134.75} \\ \\ \rightarrow \sf{\: \frac{22}{7} \red{{r}^{3} } = 134.75} \\ \\ \rightarrow \sf{ 22 {r}^{3} =\orange{ 943.25} }\\ \\ \rightarrow \sf{ \red{{r}^{3}} = 42.875} \\ \\ \rightarrow \sf{ {r}^{3} = \green{ \frac{42875}{1000} }} \\ \\ \rightarrow \sf{ {r}^{3} = { \blue{\bigg(\frac{35}{10} \bigg) }}^{3} } \\ \\ \rightarrow \: \boxed{ \sf{ r \: = \orange{3.5 \: cm}}}$

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Therefore ,

$\star \: \text{ \orange{area \: of \: base(A) }}= \sf{\red{ \pi \: {r}^{2}} } \\ \\ \rightarrow \text{A }\: = \sf{ \green{\frac{22}{7} \times 3.5 \times 3.5}} \\ \\ \rightarrow \text{ A }\: = \sf{22 \times 0.5 \times 3.5} \: \\ \: \\ \rightarrow \boxed{ \red{\text{A } = 38.5 \: {cm}^{2}} }$

Hence area of base of circular cone is

38.5 cm².

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