Advertisements
Advertisements
प्रश्न
The radii of the ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its curved surface area.
Advertisements
उत्तर
Given: Radii (r1) = 14 cm, r2 = 6 cm, height (h) = 6 cm
Slant height of the frustum (l)
= `sqrt(h^2 + (r_1 - r_2)^2)`
= `sqrt(6^2 + (14 - 6)^2)`
= `sqrt(6^2 + 8^2)`
= `sqrt(36 + 64)`
= `sqrt(100)`
= 10 cm
Curved surface area of the frustum
= πl (r1 + r2)
= 3.14 × 10 (14 + 6)
= 3.14 × 10 × 20
= 628 cm2
∴ The curved surface area of the frustum is 628 cm2.
APPEARS IN
संबंधित प्रश्न
A solid toy s in the form of a hemisphere surrounded by a right circular cone . The height of cone is 4 cm and the diameter of the base is 8 cm . Determine the volume of the toy. If a cube circumscribes the toy , then find the difference of the volumes of cube and the toy .
A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively . Find the cost of milk at the rate of ₹44 per litre which the container can hold.
A cone of radius 4 cm is divided into two parts by drawing a plane through the mid point of its axis and parallel to its base . Compare the volumes of two parts.
A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5 : 12, write the ratio of the total surface area of the cylinder to that of the cone.
A cylinder and a cone are of the same base radius and of same height. Find the ratio of the value of the cylinder to that of the cone.
The slant height of the frustum of a cone is 5 cm. If the difference between the radii of its two circular ends is 4 cm, write the height of the frustum.
The radii of the circular ends of a frustum are 6 cm and 14 cm. If its slant height is 10 cm, then its vertical height 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
In a right circular cone , the cross-section made by a plane parallel to the base is a
A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 16 cm and 12 cm. Find the capacity of the glass.
A container, open at the top, is in the form of a frustum of a cone of height 24 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 ₹21 per litre.
The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm, and its slant height is 10 cm. Find its capacity and total surface area.
A bucket made up of a metal sheet is in the form of frustum of a cone. Its depth is 24 cm and the diameters of the top and bottom are 30 cm and 10 cm, respectively. Find the cost of completely filling the bucket with milk at the rate of Rs 20 per litre and the cost of metal sheet used if it costs Rs 10 per 100 cm2.
A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively, is melted and recast in the form of a cone of base diameter 8 cm. The height of the cone is ______.
A cylinder and a cone area of same base radius and of same height. The ratio of the volume of cylinder to that of cone is ______.
In a right circular cone, the cross-section made by a plane parallel to the base is a ______.
An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder.
Find the total surface area of frustum, if its radii are 15 cm and 7 cm. Also, the slant height of the frustum is 14 cm.
Radii of the frustum = `square` cm and `square` cm
Slant height of the frustum = `square` cm
Total surface area = `π[(r_1^2 + r_2^2 + (r_1 + r_2)l]`
= `22/7 [square + square + (square + square) square]`
= `22/7 (square)`
= `square` cm2
Hence, the total surface area of the frustum is `square`.
