Bissoy.com
Doctors Medicines MCQs Q&A

The height of a solid cylinder is 48 cm and the radius of its base is 7 cm. Two identical conical holes each of radius 7 cm and slant height 25 cm are drilled out. What is the surface area (in cm2) of a newly formed solid?

The height of a solid cylinder is 48 cm and the radius of its base is 7 cm. Two identical conical holes each of radius 7 cm and slant height 25 cm are drilled out. What is the surface area (in cm2) of a newly formed solid? Correct Answer 3212 cm<sup>2</sup>

Given:

Height of Cylinder = 48 cm

Radius of Cylinder = 7 cm

Slant Height of Cone = 25 cm

Radius of Cone = 7 cm

Concept used:

The surface area of Remaining Solid = C.S.A of Cylinder + 2(C.S.A of Cone)

Where: C.S.A = Curved Surface Area

Formula used:

The curved Surface area of Cylinder = 2πRH

The curved Surface area of Cone = πrl

Where:

R = Radius of Cylinder, H = Height of Cylinder

r = Radius of Cone, l = slant height of Cone

Calculation:

[ alt="F7 Ujjwal Nautiyal 26-5-2021 Swati D2" src="//storage.googleapis.com/tb-img/production/21/05/F7_Ujjwal%20Nautiyal_26-5-2021_Swati_D2.png" style="width: 198px; height: 226px;">

 

Curved Surface area of Cylinder = 2 × (22/7) × 7 × 48 = 2112

Curved Surface area of Cone = (22/7) × 7 × 25 = 550

Surface Area of Remaining Solid = 2112 + 2(550)

⇒ 2112 + 1100 = 3212

∴ The surface area of remaining solid is 3212 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. 
The height of a solid cylinder is 30 cm and the diameter of its base is 10 cm. Two identical conical holes each of radius 5 cm and height 12 cm are drilled out. What is the surface area (in cm2) of the remaining solid?
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.
If base of right pyramid is a square and area of a slant surface of the pyramid is 24 cm2 and slant triangle perpendicular height of the pyramid is 6 cm, then what will be the ratio of total slant surface area to the base area of the pyramid?
Circular areas of same size have been marked to drill holes in a road. If the radius of one of the holes to be drilled is 21cm, and there are 10 holes to be drilled along the road, what is the total area in sq.cm of all the 10 circles marked to be drilled? (π = 22 / 7)
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.
Given below are two quantities named A and B. Based on the given information, you have to determine relation between the two quantities. You should use the given data and knowledge of Mathematics to choose between the possible answers. Quantity A: Number of hemispheres that can be formed by melting a sphere having volume equal to the volume of right circular cylinder whose diameteris 6 cm and height is 4 cm. Also, radius of hemisphere formed is half the radius of sphere from which the hemisphere is formed. Quantity B: Number of ice cream cones that can be made from a right circular cylinder shape ice cream container having radius 6 cm and height 5 cm. Ice cream cone to be made should have height 4 cm and slant height 5 cm and there should be a hemisphere made on top of the cone having radius equal to the radius of cone.
Which of the following statement(s) given below is / are TRUE? A: Volume of a cylinder with base area 38.5 cm2 and curved surface area 132 cm2 is 154 cm3. B: Total small spherical balls of radius 3 cm that can be casted after melting a large spherical ball of radius 15 cm is 25. C: Curved surface area of a cone of base radius 7 cm and height 24 cm is 540 cm2.
The total surface area of a circular base cone is 9856 cm2 and the radius of the circular base of the cone is 28 cm. If the height of a cylinder is \(83\frac{1}{3}\% \) of the slant height of the cone and the radius of cylinder is 14 cm, then what is the volume of the cylinder?
The height of a cylinder is 40% more than its radius and is equal to the radius of a right circular cone. If the curved surface area of the cone is 4400 cm2 and its radius is 87.5% of its slant height, then what is the height of the cylinder?