Question

plss solve this question

Answer 1

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Answer 2

Answer:

Area of the metalic sheet required Ab = 3351.07 cm²

Volume of the water bucket can hold V = 23728.57 cm³

Step-by-step explanation:

To find:

1) Total Surface area of the bucket = Ab

2) Volume of the bucket = Vb

Given: Bottom Diameter of the Bucket = d = 25 cm

Top Diameter of the ucket = D = 45 cm

Height of the bucket = H = 24 cm

1) Total area of metallic sheet used = Lateral area of frustum of the cone + Area of the bottom of the bucket (circular plate)

∴ Area of the frustum of the bucket is given by

Af = $\pi (R+r)\sqrt{(R-r)^{2} + H^{2} }$

∴Af = $\pi(45/2+25/2) \sqrt{(45/2-25/2)^{2} + 24^{2}}$

∴Af = (22/7)×35×[√(10²+24²)]

∴Af = 110 × √(100+ 576)

∴ Af = 110 × √676 = 110 × 26

∴ Af = 2860  cm²     ..... (1)

Area of the bottom of the circular plate = Ac

Ac = (\pi×d²) / 4

∴ Ac = (22/7) × 25² / 4 = (22/7) × 625 / 4

∴ Ac = 491.07 cm²    ...... (2)

From eq. (1) and (2) we get the total area of the bucket, i.e. Area of metalic sheet required

Ab = Af + Ac

Ab = 2860 +  491.07

Ab = 3351.07 cm²

2) Volume of the Bucket: V

Volume of the frustum of the cone is given by

V = (1/3) * H * (R² + r² + R*r)

∴ V = (π/3) * 24 * {(45/2)² + (25/2)² + (45/2*25/2)}

∴V = π8 * (2025 + 625 + 1125)/4

∴ V = (22/7) × 8 × (3775 / 4)

∴ V = 23728.57 cm³  

Volume of the water bucket can hold = 23728.57 cm³