Advertisements
Advertisements
Question
A bucket made of aluminum sheet is of height 20cm and its upper and lower ends are of radius 25cm an 10cm, find cost of making bucket if the aluminum sheet costs Rs 70 per
100 cm2
Advertisements
Solution
Given that,
The radii of the upper and lower circles of the bucket are r1 = 25 cm and r2= 10 cm respectively.
The height of the bucket = 20 cm
The slant height of the bucket
`l=sqrt(h^2+(r_1-r_2)^2`
`=sqrt(20^2+(25-10)^2`
`=sqrt(400+225)`
`=sqrt(625)`
= 25 cm
The surface area of the used aluminium sheet to make the bucket
`S=pi(r_1+r_2)xxl+pir_2^2`
= 3.14(25+10) x 25 + 3.14 x 10 x 10
= 3.14 x 35 x 25 + 3.14 x 100
= 2747.5 + 314
= 3061.5 cm
It is given that the cost of aluminium sheet is Rs 70 per 100 cm2
therefore, the total cost of making the bucket
`Rs 3061.5/100xx70`
Rs 2143.05
Hence, the total cost of making the bucket is Rs 2143.05.
APPEARS IN
RELATED QUESTIONS
Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid. [Use `pi = 22/7`]
Find the area of the shaded region in Fig. 3, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use π = 3.14]
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, find:
1) The area of the metal sheet used to make the bucket.
2) Why we should avoid the bucket made by ordinary plastic? [Use π = 3.14]
The internal and external diameters of a hollow hemisphere vessel are 21cm and 25.2 cm The cost of painting 1cm2 of the surface is 10paise. Find total cost to paint the vessel all
over______?
A solid sphere of radius 'r' is melted and recast into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 4 cm, its height 24 cm and thickness 2 cm, find the value of 'r'.
A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm2 .
From a solid cube of side 7 cm , a conical cavity of height 7 cm and radius 3 cm is hollowed out . Find the volume of the remaining solid.
Two solid cones A and B are placed in a cylindrical tube as shown in fig .16.76. The ratio of their capacities are 2: 1 . Find the heights and capacities of the cones . Also, find the volume of the remaining portion of the cylinder.
If the total surface area of a solid hemisphere is 462 cm2, then find its volume.
A rocket is in the form of a circular cylinder closed at the lower end and a cone of the same radius is attached to the top. The radius of the cylinder is 2.5 m, its height is 21 m and the slant height of the cone is 8 m. Calculate the total surface area of the rocket.
A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be poured into cylindrical bottles of diameter 5 cm and height 6 cm each. Find the number of bottles required.
If the areas of three adjacent faces of a cuboid are x, y and z, respectively, the volume of the cuboid is ______.
A container opened at the top and made up of a metal 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 ₹ 50 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 10 per 100 cm2. (Take π = 3⋅14)
Two cubes each of volume 8 cm³ are joined end to end, then the surface area of the resulting cuboid is ______.
The total surface area of a solid hemisphere of radius r is ________.
The shape of a gilli, in the gilli-danda game (see figure), is a combination of ______.
A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is `pir [sqrt(r^2 + h^2) + 3r + 2h]`.
There are two identical solid cubical boxes of side 7 cm. From the top face of the first cube a hemisphere of diameter equal to the side of the cube is scooped out. This hemisphere is inverted and placed on the top of the second cube’s surface to form a dome. Find
- the ratio of the total surface area of the two new solids formed
- volume of each new solid formed.
Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals.
500 ml milk is packed in a cuboidal container of dimensions 15 cm × 8 cm × 5 cm. These milk packets are then packed in cuboidal cartons of dimensions 30 cm × 32 cm × 15 cm.
Based on the above-given information, answer the following questions:
i. Find the volume of the cuboidal carton. (1)
ii. a. Find the total surface area of the milk packet. (2)
OR
b. How many milk packets can be filled in a carton? (2)
iii. How much milk can the cup (as shown in the figure) hold? (1)
