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 fez, the cap used by the Turks, is shaped like the frustum of a cone (see the figure given below). 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, find the area of material use for making it. [use π=22/7]
Derive the formula for the curved surface area and total surface area of the frustum of cone.
The circumferences of circular faces of a frustum are 132 cm and 88 cm and its height is 24 cm. To find the curved surface area of the frustum complete the following activity.( \[\pi = \frac{22}{7}\])
A washing tub in the shape of a frustum of a cone has a height of 21 cm. The radii of the circular top and bottom are 20 cm and 15 cm respectively. What is the capacity of the tub? ( \[\pi = \frac{22}{7}\]).
A bucket, made of metal sheet, is in the form of a cone whose height is 35 cm and radii of circular ends are 30 cm and 12 cm. How many litres of milk it contains if it is full to the brim? If the milk is sold at Rs 40 per litre, find the amount received by the person.
A bucket is in the form of a frustum of a cone and holds 15.25 litres of water. The diameters of the top and bottom are 25 cm and 20 cm respectively. Find its height and area of tin used in its construction.
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.
If a cone and a sphere have equal radii and equal volumes. What is the ratio of the diameter of the sphere to the height of the cone?
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 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.
The height of a right circular cone is 20 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be `1/8` of the volume of the given cone, then at what height above the base is the section made?
A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter `"4"2/3` cm and height 3 cm. Find the number of cones so formed.
A funnel is a combination of
A drinking glass is in the shape of the frustum of a cone of height 21 cm with 6 cm and 4 cm as the diameters of its two circular ends. Find the capacity of the glass.
A cylindrical pencil sharpened at one edge is combination of ______.
A shuttle cock used for playing badminton has the shape of a combination of ______.
The shape of a glass (tumbler) (see figure) is usually in the form of ______.
The curved surface area of a frustum of a cone is πl (r1 + r2), where `l = sqrt(h^2 + (r_1 + r_2)^2)`, r1 and r2 are the radii of the two ends of the frustum and h is the vertical height.
Find the total surface area of frustum, if its radii are 15 cm and 7 cm. Also, the slant height of the frustum is 14 cm.
Radii of the frustum = `square` cm and `square` cm
Slant height of the frustum = `square` cm
Total surface area = `π[(r_1^2 + r_2^2 + (r_1 + r_2)l]`
= `22/7 [square + square + (square + square) square]`
= `22/7 (square)`
= `square` cm2
Hence, the total surface area of the frustum is `square`.
