Question

A bucket is 32 cm in diameter at the top and 20 cm at the bottom. Find the capacity of the bucket in litres if it is 21 cm deep. Also find the cost of the tin sheet used in making the bucket at the rate of Rs 1.50 per dm^2

Answer 1

Answer:

The capacity of bucket is 45.39 liters.

Cost to making bucket is Rs 75.12

Step-by-step explanation:

A bucket is 32 cm in diameter at the top and 20 cm at the bottom.

It is shape of frustum.

We need to find the volume of frustum in litter

Formula,

$V=\frac{1}{3}\times \pi h(R^2+r^2+R\cdot r)$

Where,

R is radius of top, (R=32 cm)

r is radius of bottom, (r=20 cm)

h is height of bucket, (h=21 cm)

1000 cubic centimeter = 1 lt

Now we find the volume of bucket,

$V=\frac{1}{3}\cdot \pi \cdot 21\cdot(32^2+20^2+32\cdot 20)$

$V=\frac{1}{3}\cdot \pi \cdot 21\cdot(1024+400+640)$

$V=45389.73\text{ cm}^3$

Now we change into litter

As we know, 1000 cubic centimeter = 1 lt

1 cubic centimeter = 1/1000 lt

$45389.73 \text{ cm}^3=\frac{45389.73}{1000}\approx 45.39 \text{ Liters}$

Thus, The capacity of bucket is 45.39 liters.

Now we need to find the cost of sheet used to making the bucket.

Rate of sheet = Rs 1.50 /dm²

First we find what area of sheet used to make bucket

Sheet used area = Curved Surface area + Area of base

Curved Surface area $=\pi l (R+r)$

Where, $l=\sqrt{(R-r)^2+h^2}$

Curved Surface Area $=\pi \times \sqrt{(R-r)^2+h^2}\times (R+r)$

Curved Surface Area $=\pi \times \sqrt{(32-20)^2+21^2}\times (32+20)$

Curved Surface Area $=3951.22 \text{ cm}^2$

Area of base $=\pi r^2=\pi 20^2\approx 1256.64 \text{ cm}^2$

Area of sheet used to making bucket = 3951.22 + 1256.64 = 5207.86 cm²

Now we change square centimeter to square decimeter

1 square centimeter = 0.01 square decimeter

5207.86 cm²=0.01 x 5207.86 dm² ≈ 52.08 dm²

Cost of 1 dm² = Rs 1.50

Cost of 52.08 dm²  = 1.50 x 50.08 = Rs 75.12

Thus, Cost to making bucket is Rs 75.12

Answer 2

Answer:

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