Capacity = 36 liter , d= 32 cm ,H = ________ cm
Answers
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)V=
3
1
×πh(R
2
+r
2
+R⋅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=
3
1
⋅π⋅21⋅(32
2
+20
2
+32⋅20)
V=\frac{1}{3}\cdot \pi \cdot 21\cdot(1024+400+640)V=
3
1
⋅π⋅21⋅(1024+400+640)
V=45389.73\text{ cm}^3V=45389.73 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}45389.73 cm
3
=
1000
45389.73
≈45.39 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)=πl(R+r)
Where, l=\sqrt{(R-r)^2+h^2}l=
(R−r)
2
+h
2
Curved Surface Area =\pi \times \sqrt{(R-r)^2+h^2}\times (R+r)=π×
(R−r)
2
+h
2
×(R+r)
Curved Surface Area =\pi \times \sqrt{(32-20)^2+21^2}\times (32+20)=π×
(32−20)
2
+21
2
×(32+20)
Curved Surface Area =3951.22 \text{ cm}^2=3951.22 cm
2
Area of base =\pi r^2=\pi 20^2\approx 1256.64 \text{ cm}^2=πr
2
=π20
2
≈1256.64 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.
Step-by-step explanation: