Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Derive the formula for the volume of the frustum of a cone.
Milk in a container, which is in the form of a frustum of a cone of height 30 cm and the radii of whose lower and upper circular ends are 20 cm and 40 cm respectively, is to be distributed in a camp for flood victims. If this milk is available at the rate of Rs 35 per litre and 880 litres of milk is needed daily for a camp, find how many such containers of milk are needed for a camp and what cost will it put on the donor agency for this. What value is indicated through this by the donor agency ?
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.( \[\pi = \frac{22}{7}\])
A cone of height 20 cm and radius of base 5 cm is made up of modeling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.
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 .
The radii of the ends of a frustum of a right circular cone are 5 metres and 8 metres and its lateral height is 5 metres. Find the lateral surface and volume of the frustum.
A metallic hemisphere is melted and recast in the shape of a cone with the same base radius R as that of the hemisphere. If H is the height of the cone, then write the values of \[\frac{H}{R} .\]
A hemisphere and a cone have equal bases. If their heights are also equal, then what is the ratio of their curved surfaces?
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 tent consists of a frustum of a cone, surmounted by a cone. If the diameter of the upper and lower circular ends of the frustum be 14 m and 26 m, respectively, the height of the frustum be 8 m and the slant height of the surmounted conical portion be 12 m, find the area of the canvas required to make the tent. (Assume that the radii of the upper circular end of the frustum and the base of the surmounted conical portion are equal.)
The height of a right circular cone is 20 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be `1/8` of the volume of the given cone, then at what height above the base is the section made?
A funnel is a combination of
An oil funnel of the tin sheet consists of a cylindrical portion 10 cm long attached to a frustum of a cone. If the total height is 22 cm, the diameter of the cylindrical portion by 8 cm and the diameter of the top of the funnel be 18 cm, then find the area of the tin sheet required to make the funnel.
A cone is cut through a plane parallel to its base and then the cone that is formedon one side of that plane is removed. The new part that is left over on the other side of the plane is called ______.
The slant height of the frustum of a cone having radii of two ends as 5 cm and 2 cm respectively and height 4 cm is ______.
The base radii of two circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes are ______.
The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is ______.
The volume of the frustum of a cone is `1/3 pih[r_1^2 + r_2^2 - r_1r_2]`, where h is vertical height of the frustum and r1, r2 are the radii of the ends.
Read the following passage and answer the questions given below.
|
A 'circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people started around 250 years back, in open fields, now generally performed in tents. One such 'Circus Tent' is shown below. The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are 9 m and 30 m respectively and height of conical part is 8 m with same diameter as that of the cylindrical part, then find |
- the area of the canvas used in making the tent;
- the cost of the canvas bought for the tent at the rate ₹ 200 per sq m, if 30 sq m canvas was wasted during stitching.
If radius of the base of cone is 7 cm and height is 24 cm, then find its slant height.
