Question

The height of a cone is 16 cm and its base radius is 12 cm. Find the cost of painting the curved surface area of the cone at Rs.10per cm2( use π = 3.14 )

Answer 1

Answer:

Given :-

• The height of a cone is 16 cm and its base radius is 12 cm (use π = 3.14)

To Find :-

• What is the cost of painting of the curved surface area of the cone at Rs 10 per cm².

Formula Used :-

➦ To find slant height (l) we know that,

${\red{\boxed{\small{\bold{{(Slant\: Height)}^{2} =\: {(Height)}^{2} + {(Radius)}^{2}}}}}}$

➦ To find curved surface area of cone we know that,

${\red{\boxed{\small{\bold{C.S.A\: of\: Cone =\: {\pi}rl}}}}}$

Solution :-

First, we have to find the slant height or (l) of a cone,

Given :

• Height (h) = 16 cm
• Radius (r) = 12 cm

According to the question by using the formula we get,

↦ $\sf {(Slant\: Height)}^{2} =\: {(16)}^{2} + {(12)}^{2}$

↦ $\sf {(Slant\: Height)}^{2} =\: 256 + 144$

↦ $\sf {(Slant\: Height)}^{2} =\: 400$

↦ $\sf Slant\: Height =\: \sqrt{400}$

➪ $\sf\bold{\green{Slant\: Height =\: 20\: cm}}$

Hence, the slant height of a cone is 20 cm .

Again, we have to find the curved surface area of a cone,

Given :

• Radius (r) = 12 cm
• Slant height (l) = 20 cm
• π = 3.14

According to the question by using the formula we get,

↬ $\sf C.S.A\: of\: cone\ =\: 3.14 \times 12 \times 20$

↬ $\sf C.S.A\: of\: cone\: =\: \dfrac{314}{100} \times 12 \times 20$

↬ $\sf C.S.A\: of\: cone\: =\: \dfrac{314}{10\cancel{0}} \times 24{\cancel{0}}$

↬ $\sf C.S.A\: of\: cone\: =\: \dfrac{314}{10} \times 24$

↬ $\sf C.S.A\: of\: cone\: =\: \dfrac{314 \times 24}{10}$

↬ $\sf C.S.A\: of\: cone\: =\: \dfrac{7536}{10}$

➼ $\sf\bold{\pink{C.S.A =\: 753.6\: {cm}^{2}}}$

Hence, the curved surface area of a cone is 753.6 cm².

Now, we have to find the cost of painting of the curved surface area of the cone at Rs 10 per m²,

If, one cost of painting is Rs 10

Then, 753.6 cost of painting will be,

⇒ $\sf 753.6 \times 10$

⇒ $\sf \dfrac{7536 \times \cancel{10}}{\cancel{10}}$

➠ $\sf\bold{\purple{Rs\: 7536}}$

${\underline{\boxed{\small{\bf{\therefore The\: cost\: of\: painting\: is\: Rs\: 7536\: .}}}}}$

Answer 2

Given :

• Height of Cone is 16 cm .
• Radius of Cone is 12 cm .

To Find :

• Cost of Painting the Curved Surface Area at Rs.10 per cm² .

Solution :

Firstly we will find Slant Height of Cone :

$\longmapsto\tt\bf{{(l)}^{2}={(h)}^{2}+{(r)}^{2}}$

$\longmapsto\tt{{l}^{2}={(16)}^{2}+{(12)}^{2}}$

$\longmapsto\tt{{l}^{2}=256+144}$

$\longmapsto\tt{{l}^{2}=400}$

$\longmapsto\tt{l=\sqrt{400}}$

$\longmapsto\tt\bf{l=20\:cm}$

Now ,

$\longmapsto\tt{Radius=12\:cm}$

$\longmapsto\tt{Slant\:Height=20\:cm}$

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cone=\pi{rl}}$

Putting Values :

$\longmapsto\tt{\dfrac{314}{{\cancel{10}}{\not{0}}}\times{12}\times{{\cancel{2}}{\not{0}}}}$

$\longmapsto\tt{\dfrac{314\times{12}}{5}}$

$\longmapsto\tt{\cancel\dfrac{3768}{5}}$

$\longmapsto\tt\bf{753.6\:{cm}^{2}}$

Also ,

$\longmapsto\tt{Cost\:of\:Painting\:1\:{cm}^{2}=Rs.10}$

Cost of Painting 753.6 cm² :

$\longmapsto\tt{753.6\times{10}}$

$\longmapsto\tt\bf{Rs.7536}$