Question

Question:-

​A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is 12 per m , what will be the cost of painting all these cones? (Use π = 3.14 and take
1.04 = 1.02)

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Answer 1

Appropriate Question

A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per square m , what will be the cost of painting all these cones?

(Use π = 3.14 and take sqrt(1.04) = 1.02 )

$\large\underline{\sf{Solution-}}$

Given that

• There are 50 hollow card-board cones.

• Diameter of cone = 40 cm

• Height of cone = 1 m

Let assume that,

• Radius of cone be represented as 'r' m

• Height of cone be represented as 'h' m

• Slant height of cone be represented as 'l' m.

Now,

Given that,

Diameter of cone = 40 cm

So, Radius, r = 20 cm = 0.2 m

Height, h = 1 m

We know,

Slant height of cone is evaluated by using formula,

$\rm :\longmapsto\: {l}^{2} = {r}^{2} + {h}^{2}$

$\rm :\longmapsto\: {l}^{2} = {(0.2)}^{2} + {1}^{2}$

$\rm :\longmapsto\: {l}^{2} = 0.04 + 1$

$\rm :\longmapsto\: {l}^{2} = 0.04 + 1$

$\rm :\longmapsto\: {l}^{2} = 1.04$

$\rm :\longmapsto\: {l} = \sqrt{1.04}$

$\bf\implies \:l = 1.02 \: m$

Now, we know that

Curved Surface Area of cone is

$\underbrace{ \boxed{ \bf \: CSA_{(Cone)} = \pi \: r \: l}}$

where,

• r is radius of cone

• l is slant height

So, on substituting the values of r and l, we get

$\rm :\longmapsto\:CSA_{(Cone)} = 3.14 \times 0.2 \times 1.02$

$\rm :\longmapsto\:CSA_{(Cone)} =0.64056 \: {m}^{2}$

Now, As it is given that, there are 50 such cones.

So,

$\rm :\longmapsto\:CSA_{(50 \: Cones)} =0.64056 \times 50 = 32.028 \: {m}^{2}$

The outer side of each of the cones is to be painted and the cost of painting is Rs 12 per square metre.

So, Total cost of painting = 32.028 × 12 = Rs 384.34

Additional Information :-

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²

Answer 2

Answer:

Curved surface area of cone will be painted=πrl

h=1m;radius=

2

40

=20cm=0.2m

and let l be the slant height,

∴l

2

=h

2

+r

2

=1

2

+0.2

2

⇒l=

1+0.04

=

1

.04=1.02m (∵

1

.04=1.02 is given in the question)

⇒Curved surface area of 1 cone=πrl=(3.14×0.2×1.02)m

2

=0.64046m

2

⇒ Curved surface area of 50 cones=50×0.64046=32.028m

2

Cost of painting 1m

2

=Rs.12

∴ Cost of painting 32.028m

2

=(12×32.028)=384.336m

2

≈384.34

∴ Cost of painting 50 cones is Rs.384.84

Step-by-step explanation:

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