Advertisements
Advertisements
प्रश्न
The perimeters of the ends of a frustum of a right circular cone are 44 cm and 33 cm. If the height of the frustum be 16 cm, find its volume, the slant surface and the total surface.
Advertisements
उत्तर
The height of the frustum of the cone is h= 16 cm. The perimeters of the circular ends are 44 cm and 33 cm. Let the radii of the bottom and top circles are r1 cm and r2 cm respectively. Then, we have
2πr1= 44
⇒ πr1= 22
⇒ `r_1+(22xx7)/22`
⇒ r1 = 7
2πr2 = 33
⇒ `pi r_2=33/2`
⇒ `r_2=33/2xx7/22`
⇒ `r_2=21/4`
The slant height of the bucket is
`l=sqrt((r_1-r_2)^2+h^2)`
`=sqrt((7_21/4)^2+h^2)`
= 16.1 cm
The curved/slant surface area of the frustum cone is
`= pi(r_1+r_2)xxl`
`=(pir_1+pir_2)xxl`
= (22 + 16.5)xx16.1
= 619.85 cm2
Hence Curved surface area = 619.85cm2
The volume of the frustum of the cone is
`V=1/3pi(r_1^2+r_1r_2+r_2^2)xxh`
`=1/3pi(7^2+7xx5.25+5.25^2)xx16`
= 1900 cm3
Hence Volume of frustum = 1900cm3
The total surface area of the frustum cone is
`=pi(r_1+r_2)xxl+pi r_1^2+pi r_2^2`
`=619.85+22/7xx7^2+22/7xx5.25^2`
= 860.25 Square cm
Hence Total surface area = 860.25 cm2
APPEARS IN
संबंधित प्रश्न
The largest possible sphere is carved out of a wooden solid cube of side 7 em. Find the volume of the wood left. (Use\[\pi = \frac{22}{7}\]).
The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder. `("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:
In Fig. 5, from a cuboidal solid metallic block, of dimensions 15cm ✕ 10cm ✕ 5cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block [Use
`pi=22/7`]
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`]
From a solid right circular cylinder of height 2.4 cm and radius 0.7 cm, a right circular cone of same height and same radius is cut out. Find the total surface area of the remaining solid.
A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of cone are 6cm and 4cm. determine surface area of toy?
If the radii of circular ends of a bucket 24cm high are 5cm and 15cm. find surface area of
bucket?
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)
From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid. [User `pi22/7`]
The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid.
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
Two cubes each of volume 27 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.
Find the ratio of the volume of a cube to that of a sphere which will fit inside it.
The volume of a hemisphere is 19404 cm3. The total surface area of the hemisphere is
The total surface area of a solid hemisphere of radius 7 cm is ______.
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)
