Advertisements
Advertisements
Question
From a soild cylinder of height 20 cm and diameter 12 cm, a conical cavity of height 8 cm and radius 6 cm is hallowed out. Find the total surface area of the remaining solid.
Solution
Given, Height of cylinder h1 = 20 cm
Radius of cylinder = `12/2` = 6 cm.
Height of the cone (h2) = 8 cm.
Radius of the cone r = 6 cm.
Total surface area of remaining solid = Curved surface area of cylinder + Curved surface area of cone + Area of the top face of the cylinder
Slant height of the cone (l) = `sqrt("h"_2^2 + "r"^2)`
= `sqrt(8^2 + 6^2)`
= `sqrt(64 + 36)`
= 10 cm.
∴ Curved surface area of cone = πrl
= `22/7 xx 6 xx 10`
= `1320/7` cm2
Curved surface area of cylinder = 2πrh
= `2 xx 22/7 xx 6 xx 20`
= `5280/7` cm2
Area of the top face of the cylinder = πr2
= `22/7 xx 6 xx 6`
= `792/7` cm2
∴ Total surface area of the remaining solid
= `1320/7 + 5280/7 + 792/7`
= `7392/7`
= 1056 cm2
APPEARS IN
RELATED QUESTIONS
A spherical ball of radius 3cm is melted and recast into three spherical balls. The radii of the two of balls are 1.5cm and 2cm . Determine the diameter of the third ball?
A path 2m wide surrounds a circular pond of diameter 40m. how many cubic meters of gravel are required to grave the path to a depth of 20cm ?
The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.
The diameters of internal and external surfaces of hollow spherical shell are 10cm and 6cm respectively. If it is melted and recast into a solid cylinder of length of 2`2/3`cm, find the
diameter of the cylinder.
A metallic right circular cone 20cm high and whose vertical angle is 90° is cut into two parts at the middle point of its axis by a plane parallel to base. If frustum so obtained bee
drawn into a wire of diameter
(1/16) cm find length of the wire?
A hemispherical tank, of diameter 3 m, is full of water. It is being emptied by a pipe at the rate of \[3\frac{4}{7}\] litre per second. How much time will it take to make the tank half empty?\[\left[ Use \pi = \frac{22}{7} \right]\]
Choose the correct answer of the following question:
If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/hour. How much area will it irrigate in 30 mins; if 8 cm standing water is needed?
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is ______.
500 persons are taking a dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is 0.04m3?
