Advertisements
Advertisements
प्रश्न
In Fig. 4, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use `pi=22/7` and `sqrt5=2.236`)
Advertisements
उत्तर
The remaining solid is a frustum of the given cone
Total surface area of the frustum = πl(r1+r2)+πr12+πr22
Where
h = Height of the frustum = 12−4 = 8 cm
r1 = Larger radius of the frustum = 6 cm
r2 = Smaller radius of the frustum
l = Slant height of the frustum
In the given figure, ∆ABC ~ ∆ADE by AA similarity criterion.
`:.(BC)/(DC)=(AB)/(AD)`
`=>r_2/6=4/12`
⇒r2=2 cm
We know
`l = sqrt(h^2+(r_1-r_2)^2)`
`=>l=sqrt(8^2+(6-1)^2)`
`=>l = 4sqrt5 `
∴ Total surface area of the frustum = πl(r1+r2)+πr12+πr22
= π×4`sqrt5`(6+2)+π×62+π×22
`=pi(32sqrt5+40)`
`=22/7xx111.552`
= 350.592 cm2
Hence, the total surface area of the remaining solid is 350.592 cm2.
APPEARS IN
संबंधित प्रश्न
A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer.
150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
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]
Two cubes each of volume 27 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.
If r1 and r2 be the radii of two solid metallic spheres and if they are melted into one solid sphere, prove that the radius of the new sphere is \[\left( r_1^3 + r_2^3 \right)^\frac{1}{3}\].
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
A solid is hemispherical at the bottom and conical above. If the surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is
From a cubical piece of wood of side 21 cm, a hemisphere is carved out in such a way that the diameter of the hemisphere is equal to the side of the cubical piece. Find the surface area and volume of the remaining piece.
A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of ₹5 per 100 sq cm. [Use ππ = 3.14]
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm, respectively. The radii of the hemispherical and the conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.
In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here?
A right triangle whose sides are 15 cm and 20 cm (other than hypotenuse), is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate)
Find the ratio of the volume of a cube to that of a sphere which will fit inside it.
A plumbline (sahul) is a combination of
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)
The shape of a gilli, in the gilli-danda game (see figure), is a combination of ______.
Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr2.
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]`.
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)
