Use unless stated otherwise.
Capacity of the glass,
Here, R = 2 cm , r = 1 cm , h = 14 cm
Therefore Â Â Â
Q.2 Â Â The slant heightÂ of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. FindÂ the curved surface areaÂ of the frustum.
Sol.
Slant height ,l = 4 cm (Given)
Â Â Â Â Â Â Â Â Â
andÂ Â Â Â Â Â Â Â Â Â
Curved surface of theÂ frustum
Q.3Â Â Â Â Â A fez, theÂ (cap) used by the Turks, isÂ shaped like the frustum of a cone (see figure). If its radius on the open side is 10 cm, radius at the upper base is 4 cmand its slant height is 15 cm, find the area of material used forÂ making it.
Sol.Â
HereÂ R = 10 cm, r = 4 cm and l = 15 cm
Area of the material used for making the feza = Surface area of frustum
+Â TheÂ surface of top circular section
Q.4Â Â Â Â Â A containerÂ opened fromÂ the top and made up of a metalÂ sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of milk which can completely fill the container, at the rate of Rs 20 per litre. AlsoÂ find theÂ cost of metal sheet used to make the container, if it costs Rs 8 per 100 . (Take ).
Sol.Â
Here R = 20 cm, r = 8 cm and h = 16 cm Capacity of the container
= Volume of the frustum
Cost of milk @ Rs 20 per litre
To find the slant height
and area of the bottom
ThereforeÂ Total area of metal required Â
= 1758.4
Cost of metal sheet used to manufacture the container @ Rs 8 per
Let ABC be the metallic cone, DECB is the required frustum.
Let the twoÂ radii of the frustum be
From the s ADO' and ABO,
Volume of theÂ frustum DBCE
Volume of the wireÂ of length l andÂ diameter D
Â Â Â Â Â Â
ThereforeÂ Volume of the frustum = VolumeÂ of the wire drawn from it
Â Â Â Â Â Â Â Â Â
Â Â Â
Â Â Â Â Â Â = 7964.44 m