A bucket is in the form of a frustum of a cone of height 30 cm with radii of its - Maths - Surface Areas and Volumes

Question

A bucket is in the form of a frustum of a cone of height
30 cm with radii of its lower and upper ends as 10 cm and 20 cm
respectively Find the capacity and surface area of the bucket Also
find the cost of milk which can completely fill the container at
the rete of Rs 25 per litere (Pie = 22/7)

Rayya Halim · Accepted Answer

capacity or volume of a frustum of a cone is given by

$V = \frac{Π h}{3} (R^{2} + r^{2} + R r)$

here we have R= 20cm r = 10 cm , h = 30 cm

putting all these values in the volume formula

$V = \frac{Π \times 30}{3} (20^{2} + 10^{2} + 20 \times 10) = \frac{22 \times 10 (400 + 100 + 200)}{7} V = 22000 {c m}^{3} = 22 l t r$

Now the for the surface area calculate first the slant height l

using Pythagorean theorem as

$l^{2} = h^{2} + {(R - r)}^{2} l = \sqrt{30^{2} + 10^{2}} = 10 \sqrt{10}$

now surface area is given as

$b a s e a r e a s = Π R^{2} + Π r^{2} = 500 Π$

and total surface area is

$A = b a s e a r e a s + Π (R + r) l = 500 Π + 948.68 Π = 4552.9 {c m}^{2}$

Now the capacity of the bucket is 22 ltr

so cost of 1 ltr milk is Rs 25 so

cost of 22 Ltr milk will be = 25×22 Rs.

= Rs. 550

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A bucket is in the form of a frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the capacity and surface area of the bucket. Also find the cost of milk which can completely fill the container at the rete of Rs.25 per litere . (Pie = 22/7).