Advertisements
Advertisements
प्रश्न
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.( \[\pi = \frac{22}{7}\])
Advertisements
उत्तर
(Circumference)1 = 2πr1 = 132
∴ r1 = `132/(2π) = (132 xx 7)/(2 xx 22)` = 21 cm
(Circumference)1 = 2πr2 = 88
r2 = `88/(2π) = (88 xx 7)/(2 xx 22)`
= 14 cm
Slant height of frustum, `l = sqrt(h^2 + (r_1 - r_2)^2`
= `sqrt((24)^2 + (21 - 14)^2`
= `sqrt((24)^2 + (7)^2`
= `sqrt(576 + 49)` = `sqrt(625)`
= `sqrt(25 xx 25)` = 25 cm
Curved surface area of the frustum = `π(r_1 + r_2)l`
= `22/7 (21 + 14) xx 25`
= `22/7 xx 35 xx 25`
= 2750 cm2
संबंधित प्रश्न
A container, opened from 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 the milk which can completely fill the container, at the rate of Rs.20 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs.8 per 100 cm2. [Take π = 3.14]
Derive the formula for the volume of the frustum of a cone.
A metal container, open from the top, is in the shape of a frustum of a cone of height 21 cm with radii of its lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs 35 per litre.\[\left[ Use \pi = \frac{22}{7} \right]\]
A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm respectively. Find :
(i) the volume of water which can completely fill the bucket.
(ii) the area of the metal sheet used to make the bucket.
[Use π =\[\frac{22}{7}\]
The surface area of a sphere is the same as the curved surface area of a cone having the radius of the base as 120 cm and height 160 cm. Find the radius of the sphere.
A frustum of a cone is 9 cm thick and the diameters of its circular ends are 28 cm and 4 cm. Find the volume and lateral surface area of the frustum.
(Take π = 22/7).
An oil funnel of tin sheet consists of a cylindrical portion 10 cm long attached to a frustum of a cone. If the total height be 22 cm, the diameter of the cylindrical portion 8 cm and the diameter of the top of the funnel 18 cm, find the area of the tin required.(Use π = 22/7).
An icecream cone full of icecream having radius 5 cm and height 10 cm as shown in fig. 16.77. Calculate the volume of icecream , provided that its 1/ 6 part is left unfilled with icecream .
A hemisphere and a cone have equal bases. If their heights are also equal, then what is the ratio of their curved surfaces?
If r1 and r2 denote the radii of the circular bases of the frustum of a cone such that r1 > r2, then write the ratio of the height of the cone of which the frustum is a part to the height fo the frustum.
A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. The radius of the cone is
The height and radius of the cone of which the frustum is a part are h1 and r1 respectively. If h2 and r2 are the heights and radius of the smaller base of the frustum respectively and h2 : h1 = 1 : 2, then r2 : r1 is equal to
A tent is made in the form of a frustum of a cone surmounted by another cone. The diameters of the base and the top of the frustum are 20 m and 6 m, respectively, and the height is 24 m. If the height of the tent is 28 m and the radius of the conical part is equal to the radius of the top of the frustum, find the quantity of canvas required. `["Take" π = 22/7.]`
The perimeters of the two circular ends of a frustum of a cone are 48 cm and 36 cm. If the height of the frustum is 11 cm, then find its volume and curved surface area.
A milk container is made of metal sheet in the shape of frustum of a cone whose volume is `"10459" 3/7 "cm"^3`. The radii of its lower and upper circular ends are 8 cm and 20 cm, respectively. Find the cost of metal sheet used in making the container at the rate of ₹ 1.40 per cm2.
The shape of a glass (tumbler) is usually in the form of ______.
A cone is cut by a plane parallel to its base and the upper part is removed. The part that is left over is called ______.
A shuttle cock used for playing badminton has the shape of a combination of ______.
A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form a cone of base diameter 8 cm. The height of the cone is ______.
