Advertisements
Advertisements
Question
Advertisements
Solution
Radius of one circular end, r1 = 14 cm
Radius of other circular end, r2 = 7 cm
Height of the bucket, h = 30 cm
∴ Volume of water in the bucket = Volume of frustum of cone
\[= \frac{1}{3}\pi h\left( r_1^2 + r_1 r_2 + r_2^2 \right)\]
\[ = \frac{1}{3} \times \frac{22}{7} \times 30 \times \left( {14}^2 + 14 \times 7 + 7^2 \right)\]
\[ = \frac{1}{3} \times \frac{22}{7} \times 30 \times 343\]
\[ = 10780 {cm}^3\]
\[= \frac{10780}{1000}\] ...[∵ 1 litre = 1000cm3]
= 10.78 L
Thus, the bucket can hold 10.78 litres of water.
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 ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its total surface area.
A solid toy s in the form of a hemisphere surrounded by a right circular cone . The height of cone is 4 cm and the diameter of the base is 8 cm . Determine the volume of the toy. If a cube circumscribes the toy , then find the difference of the volumes of cube and the toy .
A solid cone of base radius 10 cm is cut into two part through the mid-point of its height, by a plane parallel to its base. Find the ratio in the volumes of two parts of the cone.
An icecream cone full of icecream having radius 5 cm and height 10 cm as shown in fig. 16.77. Calculate the volume of icecream , provided that its 1/ 6 part is left unfilled with icecream .
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 \[\frac{H}{R} .\]
A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5 : 12, write the ratio of the total surface area of the cylinder to that of the cone.
If the areas of circular bases of a frustum of a cone are 4 cm2 and 9 cm2 respectively and the height of the frustum is 12 cm. What is the volume of the frustum?
The slant height of the frustum of a cone is 5 cm. If the difference between the radii of its two circular ends is 4 cm, write the height of the frustum.
The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is 5 cm, then height of the cone is
The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is
The radii of the circular ends of a frustum are 6 cm and 14 cm. If its slant height is 10 cm, then its vertical height is
A hemisphere of lead of radius 9 cm is cast into a right circular cone of height 72 cm. Find the radius of the base of the cone.
A container, open at the top, is in the form of a frustum of a cone of height 24 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 ₹ 21 per litre.
A bucket is in the form of a frustum of a cone. Its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. Find how many litres of water the bucket can hold. `["Take" π = 22/7.]`
The perimeters of the two circular ends of a frustum of a cone are 48 cm and 36 cm. If the height of the frustum is 11 cm, then find its volume and curved surface area.
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 fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is
4 cm and its slant height is 15 cm, then find the area of material used for making it. `["Use" π = 22/7.]`
A right cylindrical vessel is full of water. How many right cones having the same radius and height as those of the right cylinder will be needed to store that water?
The circular ends of a bucket are of radii 35 cm and 14 cm and the height of the bucket is 40 cm. Its volume is ______.
