A solid cylinder of silver 9 cm high and 4 cm in diameter is melted and recasted into a right circular cone of diameter 6 cm. Find height and total surface area of the come. π=3.14
Answers
Answer:
I hope this may be helpful to you...
MARK ME AS BRAINLIEST...
Given,
Height of a solid cylinder = 9 cm
Diameter of the solid cylinder = 4 cm
Diameter of the recasted right circular cone = 6 cm
To find,
(a) The height of the cone
(b) Total surface area of the cone
Solution,
We can simply solve this mathematical problem using the following process:
Let us assume that the height of the cone formed is x cm.
As per mensuration;
Volume of a cylinder = π.(radius)^2.(height)
Volume of a right circular cone= 1/3×π.(radius)^2.(height)
Slant height of a cone = l = √((height)^2 + (radius)^2
Total surface area of a cone = π(radius)(slant height+ radius)
{Statement-1}
According to the question;
Diameter of the solid cylinder = 4 cm
=> Radius of the solid cylinder = (diameter)/2 = (4 cm)/2 = 2 cm
And, the diameter of the recasted right circular cone = 6 cm
=> Radius of the recasted right circular cone = diameter/2 = (6 cm)/2 = 3 cm
Now, according to the question;
Volume of the initial cylinder = Volume of the right circular cone formed
=> π.(radius of cylinder)^2.(height of the cylinder)
= 1/3×π.(radius of the cone)^2.(height of the cone)
{according to statement-1}
=> (2 cm)^2.(9 cm) = 1/3×(3 cm)^2.(x cm)
=> 4 cm^2 × 9 cm = 1/3 × 9 cm^2 × x cm
=> 36 cm^3 = 3 cm^3 × x cm
=> x = (36/3) cm = 12 cm
=> x = 12 cm
=> height of the cone = 12 cm
Now, the slant height of the cone formed
= √{(height)^2 + (radius)^2}
{according to statement-1}
= √((12 cm)^2 + (3 cm)^2
= √(144 cm^2 + 9 cm^2)
= √(153 cm^2) = 12.37 cm
Now, according to statement-1;
Total surface area of the cone
= π(radius)(slant height+ radius)
= 22/7 × 3 cm × (12.37 cm + 3 cm)
= 22/7 × 3 cm × (15.37 cm)
= 144.9 cm^2
Hence, the height of the cone is 12 cm and the total surface area of the cone is equal to 144.9 cm^2, respectively.