Bissoy.com
Doctors Medicines MCQs Q&A

If two conical pieces of wood are cut out from a cylindrical piece of wood from two ends whose radius and height are 7cm and 10cm, then find the total surface area of the remaining part where the radius of the conical part is the same as the radius of the cylinder and the height of the cone is 60% less than the height of the cylindrical part.

If two conical pieces of wood are cut out from a cylindrical piece of wood from two ends whose radius and height are 7cm and 10cm, then find the total surface area of the remaining part where the radius of the conical part is the same as the radius of the cylinder and the height of the cone is 60% less than the height of the cylindrical part. Correct Answer 44 (10 + √65) cm<sup>2</sup>

Given:

The radius and height of cylindrical wood are 7cm and 10cm

The radius of conical part is same as the radius of cylinder

The height of cylinder is 60% less than the height of cylindrical part.

Calculation:

According to question,

Radius of cone = 7cm

And height of cone = 10 × 40% = 4

So, the slant height of cone = √(72 + 42) = √65

Now, the required surface area of the remaining part = 2πr h + 2 × πrl

So, 2 × 22/7 × 7 (10 + √65)

Hence, 44 (10 + √65) cm2

Related Questions

“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m. 
Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relation among the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. The options represent the relations among three quantities. A. < B. > C. ≤ D. ≥ E. = Quantity 1: There is a square field of side 4 meter. A flower bed is to be prepared in its centre, leaving a gravelled path of uniform length around the flowerbed. The cost of preparing the flowerbed and gravelling the path is Rs. 100 and Rs. 200 per square meter respectively. If the total cost is Rs. 1756 then find the double of  width of gravelled path. Quantity 2: The height of a cone is 45 cm. A small cone is cut from it parallel to the base. If the ratio of volume of small cone and the remaining part is 8 : 19 then what is the height from the base from where the cone was cut? Quantity 3: A cylindrical container of radius 60 cm and height 150 cm is filled with ice cream. 10 cones of equal volume need to be prepared from the whole ice-cream. These cones has hemispherical top and the height of the conical portion is 4 times the radius of hemisphere. Find radius of the hemisphere. 
Parth had the cylindrical iron piece. He drilled out a conical cavity from the iron piece. The height and radius of the conical cavity is 15 cm and 8 cm respectively which is equal to the eight and radius of cylindrical iron piece. Find the total surface area of the remaining cylindrical iron piece.
In this question two quantities are given. Find and compare them and choose the appropriate options. A cylinder of radius R and height H has the same volume as that of a sphere of radius r. The surface area of sphere is more than the curved surface area of cylinder. Quantity I: x, where 9x – 2 = 0 Quantity II: R/H; where a cylinder of radius R and height H has the same volume as that of a sphere of radius r. The surface area of sphere is more than the curved surface area of cylinder.
From a large cone of volume 600 cm3, a small cone is cut whose height is 70% of the height of the large cone. If the radius of the small cone is 50% of the radius of the large cone, then find the volume of the remaining part left after cutting the small cone.
Historically, the production of wood charcoal in locations where there is an abundance of wood dates back to a very ancient period, and generally consists of piling billets of wood on their ends so as to form a conical pile, openings being left at the bottom to admit air, with a central shaft to serve as a flue. The whole pile is covered with turf or moistened clay. The firing is begun at the bottom of the flue, and gradually spreads outwards and upwards. The success of the operation depends upon the rate of the combustion. Under average conditions, 100 parts of wood yield about 60 parts by volume, or 25 parts by weight, of charcoal; small-scale production on the spot often yields only about 50%, while large-scale became efficient to about 90% even by the seventeenth century. The modern process of carbonizing wood, either in small pieces or as sawdust in cast iron retorts, is extensively practiced where wood is scarce, and also for the recovery of valuable byproducts (wood spirit, pyroligneous acid, wood tar), which the process permits. The information given, if accurate, most strongly supports which of the following?
The curved surface area of cylinder A is 8% more than the curved surface area of cylinder B. If the height of cylinder A is 4% less than the height of cylinder B, then the volume of cylinder A is what percentage more/less than the volume of cylinder B?
Curved surface area of Cone P is seven times the curved surface area of Cone Q. Slant height of Cone Q is seven times the slant height of Cone P. What will be the ratio of the area of the base of Cone P to the area of the base of Cone Q?
A vessel is in the form cylinder at the bottom and cone on the upper side. The ratio of height of cylinder and height of cone is 5 : 6. Total height of vessel is 44 cm. The radius of cylindrical part and conical part is same which is 7 cm. Find the curved surface area of a vessel.
Which of the following statements is/are true? A: If radius of a cylinder is decreased by 50% and its volume remains same, then its height will be increased by 200%. B: Difference between the curved surface area and total surface area of a cone is equal to the area of its circular base. C: If height of a cylinder is equal to its radius, then its curved surface area will be equal to the total area of its both the circular bases.