a bucket i sin the form of frustum with the capacity of 12308 8 cm cube the radii of the - Maths - Surface Areas and Volumes

Question

a bucket i sin the form of frustum with the capacity of 12308 8
cm cube the radii of the top and bottom of circular ends are 12 cm
and 20 cm resp find the hieght of the bucket and also the area of
metal sheets used in making the bucket (use pie=3 14)

Shridhar Kaushik · Accepted Answer

Given that Volume of the frustum (V) = 12308 8 cm3 Also, radii of the top (r1) = 12 cm Radii of the bottom (r2) = 20 cm

We know that Volume of frustum, $V = \frac{1}{3} π h (r_{1}^{2} + r_{2}^{2} + r_{1} r_{2}) \Rightarrow 12308 8 = \frac{1}{3} \times 3 14 \times h (144 + 400 + 240) \Rightarrow h = \frac{12308 8 \times 3}{3 14 \times 784} \Rightarrow h = 15 cm$ Also, we know that $l^{2} + h^{2} + (r_{1} - r_{2})^{2} \Rightarrow l^{2} = 225 + 64 \Rightarrow l^{2} = 289 \Rightarrow l = 17 cm$ Now, the bucket will be open at the top and so the area of metal sheet used in making the bucket (Say A) A = lateral surface of the frustum + (Area of circle at the bottom with r2 = 20 cm) $A = π (r_{1} + r_{2}) l + π r_{2}^{2} = 3 14 \times (12 + 20) \times 17 + 3 14 \times (20)^{2} = 3 14 \times 32 \times 17 + 3 14 \times 400 = 1708 16 + 1256 = 2964 16 {cm}^{2}$

a bucket i sin the form of frustum with the capacity of 12308.8 cm cube.the radii of the top and bottom of circular ends are 12 cm and 20 cm resp.find the hieght of the bucket and also the area of metal sheets used in making the bucket.(use pie=3.14)