A bucket has top and bottom diameter of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm² . (Use π = 3.14)
Answers
Answer:
Volume of the bucket = 8.792 dm³ and the total cost of the tin sheet used for making the bucket is ₹ 21.40.
Step-by-step explanation:
SOLUTION :
Diameter of top of bucket = 40 cm
Radius of top , R = 40/2 = 20 cm = 20/10 = 2 dm
[1 cm = 1/10 dm ]
Radius of top of bucket, R = 2 dm
Diameter of Bottom of bucket = 20 cm
Radius of Bottom ,r = 20/2 = 10 cm = 10/10 = 1 dm
Radius of bottom of bucket, r = 1 dm
Height of bucket ,h = 12 cm = 1.2 dm
Slant height of the bucket,l = √ (R - r)² + h²
= √(2 - 1)² + (1.2)²
= √1 + 1.44
= √2.44
= 1.56 dm
slant height ,l = 1.56 dm
Volume of the bucket = 1/3πh(R² + r² + Rr)
= ⅓ × 3.14×1.2(2² + 1² + 2×1)
= ⅓ × 3.14 × 1.2(4 + 1 + 2)
= ⅓ × 3.14 × 1.2 × 7
= 3.14 × 0.4 × 7
Volume of the bucket = 8.792 dm³
Area of the tin sheet used for bucket = Curved surface area of the bucket + Area of the base
= π(R + r)l + πr²
= 3.14 × (2 + 1) × 1.56 + 3.14 ×1²
= (3.14 × 3 × 1.56) + 3.14
= 14.6952 + 3.14
= 17.8352 dm²
Area of the tin sheet used for bucket = 17.8352 dm²
Rate of tin sheet = ₹ 1.2 per dm²
Total cost of the tin sheet used for making the bucket = 17.8352 × 1.2 = ₹ 21.40
Hence, Volume of the bucket = 8.792 dm³ and the total cost of the tin sheet used for making the bucket is ₹ 21.40.
HOPE THIS ANSWER WILL HELP YOU...
the radius of the top part be 'R' and radius of the bottom part be 'r' respectively.
Diameter (Top) = 40
cm Radius (R) = 40/2 =
20 cm 10 cm = 1 dm 20 cm = 2dmDiameter
(Bottom) = 20 cmRadius (r) = 20/2 =
10 cm 10 cm = 1 dmHeight = 12 cm = 1.2
dmSlant height ('l')
= √H² + (R - r)²= √(1.2)²
+ (2 - 1)²= √1.44 +
1= √2.44= 1.56So, slant height
(l) is 1.56 dmArea of the tin sheet used for bucket = Curved surface area of the bucket + Area of the base= π(R + r)*l + πr²⇒
3.14*(2 + 1)*1.56 +
3.14*1²⇒(3.14*3*1.56) +
3.14⇒ 14.6952 + 3.14⇒
17.8352 sq dmCSA of
the tin sheet used =
17.8352 sq dmRate of tin sheet = Rs. 1.2 per
sq dmTotal cost of the tin sheet used for making the bucket =
17.8352*1.2= Rs. 21.40Volume = 1/3πh(R² + r² + R*r)=
1/3*3.14*1.2*(2² + 1² +
2*1)= 1/3*3.14*1.2*7=
26.376/3Volume = 8.792 cu dm
hope it helps:---