Question

The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, then the area of the metal sheet used to make the bucket is _____. (Use $\pi$ = 3.14)

• A. $1711.3c{m}^2$
• B. $17.113m^2$
• C. $1.7113m^2$
• D. $1711.3m{m}^2$

Answer 1

The correct option is A $1711.3c{m}^2$

Given,
Height of frustum, h=24 cm
Diameter of lower end, d =10 cm
So, Radius of lower end, r = 5 cm
Diameter of upper end D = 30 cm
So, Radius of upper end, R=15 cm

Slant height of the frustum, $l=\sqrt{h^2+(R-r{)}^2}$
$=\sqrt{(24{)}^2+(15-5{)}^2}$
$=\sqrt{576+100}$
$=\sqrt{676}$
$=26cm$

Area of metal sheet used to make the bucket
= Curved surface area of frustum + Area of base
$=\pi l(R+r)+\pi r^2$
$=\pi \left[26\right(15+5)+(5{)}^2]$
$=3.14(520+25)$
$=3.14\times 545$
$=1711.3c{m}^2$