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
In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 3.5 cm. Find the total surface area of the bock `(Use pi=22/7)`
The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is:
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. [Use `pi = 22/7`]
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
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 tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m , the height of the frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent. (Take : π = 22/7)
A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 `3/7` cm3. The radii of its lower and upper circular ends are 8cm and 20cm. find the cost of metal sheet used in making container at rate of Rs 1.4 per cm2?
A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of `3/2` cm and its depth is `8/9 `cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.
In Fig. 6, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. `[\text\ User=22/7]`
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 \[\left( r_1^3 + r_2^3 \right)^\frac{1}{3}\].
A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, the radius of the base of the cone is
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.
The radius of spherical balloon increases from 8 cm to 12 cm. The ratio of the surface areas of balloon in two cases is ______.
The curved surface area of glass having radii 3 cm and 4 cm respectively and slant height 10 cm is ______.
If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is ______.
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.
The total surface area of a solid hemisphere of radius 7 cm is ______.
The ratio of total surface area of a solid hemisphere to the square of its radius is ______.
