Advertisements
Advertisements
Question
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
Solution
(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
RELATED QUESTIONS
A washing tub in the shape of a frustum of a cone has a height of 21 cm. The radii of the circular top and bottom are 20 cm and 15 cm respectively. What is the capacity of the tub? ( \[\pi = \frac{22}{7}\]).
A bucket, made of metal sheet, is in the form of a cone whose height is 35 cm and radii of circular ends are 30 cm and 12 cm. How many litres of milk it contains if it is full to the brim? If the milk is sold at Rs 40 per litre, find the amount received by the person.
A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find the radius of the base.
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.
If a cone of radius 10 cm is divided into two parts by drawing a plane through the mid-point of its axis, parallel to its base. Compare the volumes of the two parts.
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).
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. What is the ratio of their volumes?
If the areas of circular bases of a frustum of a cone are 4 cm2 and 9 cm2 respectively and the height of the frustum is 12 cm. What is the volume of the frustum?
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 diameters of the ends of a frustum of a cone are 32 cm and 20 cm. If its slant height is 10 cm, then its lateral surface area is
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.
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 right cylindrical vessel is full of water. How many right cones having the same radius and height as those of the right cylinder will be needed to store that water?
The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 cm, respectively. Find the slant height of the frustum.
A frustum of a right circular cone is of height 16 cm with radius of its ends as 8 cm and 20 cm. Then, the volume of the frustum 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.
A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.
A milk container of height 16 cm is made of metal sheet in the form of 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 ₹ 22 per litre which the container can hold.
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`.
If radius of the base of cone is 7 cm and height is 24 cm, then find its slant height.
