A bucket is in the form of a frustum of a cone with a capacity of 1230

1.	A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm3 of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of the metal sheet used in its making.(use π = 3.14)
Answer» Volume of the frustum = \(\frac{1}3π(r'^2 + r"^2 + r'r")h\) = 12308.8 ⇒ \(\frac{1}3π(20^2 + 12^2 + (20)(12))h\) = 12308.8 ⇒ h = 15 cm Let l be the slant height of the bucket ⇒ Slant height, l = \(\sqrt{(r' - r")^2 + h^2}\) ⇒ l = \(\sqrt{(20 - 12)^2 + 15^2}\) ⇒ l = 17 cm ∴ length of the bucket, l = 17 cm Curved surface area = π(r’ + r’’)l + πr’’² = π(20 + 12)(17) + π (12)² = 2160.32 cm²

A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm3 of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of the metal sheet used in its making.(use π = 3.14)

Answer»

Volume of the frustum = \(\frac{1}3π(r'^2 + r"^2 + r'r")h\) = 12308.8

⇒ \(\frac{1}3π(20^2 + 12^2 + (20)(12))h\) = 12308.8

⇒ h = 15 cm

Let l be the slant height of the bucket

⇒ Slant height, l = \(\sqrt{(r' - r")^2 + h^2}\)

⇒ l = \(\sqrt{(20 - 12)^2 + 15^2}\)

⇒ l = 17 cm

∴ length of the bucket, l = 17 cm

Curved surface area = π(r’ + r’’)l + πr’’²

= π(20 + 12)(17) + π (12)²

= 2160.32 cm²