A right angled triangle whose sides are 3 cm, 4 cm and 5 cm is revolved about the sides containing
Answers
Answer:
The difference in volumes of the two cones so formed is 4 π cm³ and the curved surfaces are 20 π cm² & 15 π cm².
Step-by-step explanation:
Given:
Case : 1
When the right angled triangle is revolved around the side 3 cm
Radius of the cone , r = 4 cm
Height of the cone , h = 3 cm
Slant height of the cone , l = 5 cm
Volume of the cone = ⅓ × πr²h
= ⅓ π × 4² × 3 = 16π cm³
Volume of the cone = 16π cm³
Curved surface area = πrl
= π × 4 × 5 = 20π cm²
Curved surface area = 20π cm²
Case 2 :
When the right angled triangle is revolved around the side 4 cm
Radius of the second cone, r = 3 cm
Height of the cone, h = 4 cm
Slant height of the cone , l = 5 cm
Volume of the cone = ⅓ × πr²h
⅓ × π × 3² × 4 = 12π cm³
Volume of the cone = 12π cm³
Curved surface area = πrl
= π × 3 × 5 = 15 π cm²
Curved surface area = 15 π cm²
Difference of the volumes of two cone = (16 - 12) πcm³ = 4π cm³
Hence, the difference in volumes of the two cones so formed is 4 π cm³ and the curved surfaces are 20 π cm² & 15 π cm².
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