8. From a solid cylinder of height 7 cm and base diameter 12 cm, a
conical cavity of same height and same base diameter is hollowed out
Find the total surface area of the remaining solid.
[Use T=1
(2012
Answers
Total Surface Area = 551 cm^2
Given:
Height of the cylinder = 7 cm
Base diameter of the cylinder = 12 cm
Calculating the radius by dividing by 2:
= 12 / 2
= 6 cm
To Find:
Remaining Total Surface Area Of The Solid
Calculating:
Calculating the slant height of the cone:
Formula used to calculate the slant height of a cone:
Slant Height = √(r^2 + h^2)
Substituting the values into the formula we get:
= √(6^2 + 7^2)
= √(36 + 49)
= √(85)
= 9.22 centimetre (Approximately)
Formula used for calculating the total surface area of the remaining solids:
= 2πrh + πrl + πr^2
Substituting all the values known to us in this formula we get:
(Here we are taking the value of pi as 22/7 and solving)
= 2 x 22/7 x 6 x 7 + 22/7 x 6 x 9.22 + 22/7 x 6 x 6
= 264 + 173.86 + 113.14
= 287 + 264
= 551 cm^2
Hence, the Total Surface Area Of The Remaining Solid is 551 cm^2.
