Advertisements
Advertisements
Question
A container in the shape of a frustum of a cone having diameters of its two circular faces as 35 cm and 30 cm and vertical height 14 cm,
is completely filled with oil. If each cm3 of oil has mass 1.2 g, then find the cost of oil in the container if it costs ₹40 per kg.
Solution
We have,
Height, h = 14 cm
Rdius of upper end, `"R"=35/2 = 17.5 "cm" and`
Radius of lower end, `r = 30/2 = 15 "cm"`
Now,
Volume of the container `= 1/3pi"h"("R"^2+"r"^2+"Rr")`
`= 1/3xx22/7xx14xx(17.5^2+15^2+17.5xx15)`
`= 44/3 xx (306.25 + 225 + 262.5)`
`=44/3xx793.75`
`=34925/3 "cm"^3`
So, the mass of the oil that is completely filled in the container`= 34925/3 xx 1.2`
= 13970 Kg
= 13.97 Kg
∴ The cost of the oil in the container = 40 ×1.2
= 13970 Kg
= 13.97
∴ The cost of the oil in the container = 40 × 13.97 = ₹ 558.80
APPEARS IN
RELATED QUESTIONS
A metal container, open from the top, is in the shape of a frustum of a cone of height 21 cm with radii of its lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs 35 per litre.\[\left[ Use \pi = \frac{22}{7} \right]\]
The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area.
A cone of radius 4 cm is divided into two parts by drawing a plane through the mid point of its axis and parallel to its base . Compare the volumes of two parts.
A metallic hemisphere is melted and recast in the shape of a cone with the same base radius R as that of the hemisphere. If H is the height of the cone, then write the values of \[\frac{H}{R} .\]
If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, the ratio of the volumes of the upper part and the cone is
A solid metallic right circular cone 20 cm high and whose vertical angle is 60°, is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter `1/12` cm, then find the length of the wire.
A shuttlecock used for playing badminton has the shape of the combination of ______.
The slant height of a frustum of a cone is 4 m and the perimeter of circular ends is 18 m and 16 m. Find the cost of painting its curved surface area at ₹ 100 per sq. m
A cone is cut through a plane parallel to its base and then the cone that is formedon one side of that plane is removed. The new part that is left over on the other side of the plane is called ______.
