a cone has been scooped out of a wooden hemisphere of diametre 14cm.the radius and hieght of the conal cavity is 1 cm less than the radius of the hemisphere .find the volume in the resulting solid?
Answers
Answer:572 cm²
Step-by-step explanation:
Let the radius of the cylindrical part as well as hemispherical part is
Given the diameter of the hemisphere part is 14 cm.
⇒ 2 = 14
⇒ = 7 cm
Here we can also say height of hemisphere is 7 cm which is radius of the
hemisphere.
Now let the height of the cylindrical part be ℎ. Given height of the vessel is
13 cm, hence height of the cylindrical part ℎ = 13 − 7 = 6 cm.
We know, inner surface area of the hemisphere = 2πr² and inner surface area of
the cylinder = 2πrh.
Total inner surface area of the vessel = Inner surface area of the hemisphere +
Inner surface area of the cylindrical part
Total inner surface area of the vessel = 2πr² + 2πrh.
Total inner surface area of the vessel = 2 × 22
7
× 7 × 7 + 2 × 22
7
× 7 × 6
= 44(7 + 6) = 572 cm²