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 m Square, what will be the cost of painting all these cones?

❌No Spam❌
Explanation Needed.​

Answer 1

$diameter \: of \: cone = 40cm$

$radius \: of \: a \: cone \: (r) = \frac{40}{2} = 0.2m$

$height \: of \: cone = 1m$

$slant \: height \: of \: a \: cone = \sqrt{r}^{2}{h}^{2}$

$= \sqrt({ {0.2}^{2} }) + {(1)}^{2}$

$= \sqrt{0.04} + 1 = \sqrt{1.64}m$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1.02m$

$csa \: of \: cone \: = \pi \: rl$

$\: \: \: \: \: \: \: \: \: \: \: \: = 3.14 \times 0.2 \times 1.02$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 0.64.056 \: {m}^{2}$

$cost \: of \: painting \: {1m}^{2}of \: a \: cone = rs.12$

$cost\:of \: 50 \: such \: boxes \: = 50x$

$7.68672 = rs.384.34$

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