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Answer:
756πcm³
Step-by-step Explanation:
The volume of the solid shape = volume of cone + volume of the hemisphere.
==> 270πcm³ + ½(4/3*π*r³)
To calculate the volume of the hemisphere, we need to get the radius of the hemisphere = the radius of the cone.
Since volume of cone = 270πcm³, we can find r using the formula for the volume of cone.
==> Volume of cone = ⅓πr²h
⅓*π*r²*10 = 270π
⅓*10*r²(π) = 270 (π)
10/3 * r² = 270
r² = 270 * ³/10
r² = 81
r = √81
r = 9 cm
Thus, volume of hemisphere = ½(4/3*π*r³)
==> Volume of hemisphere = ½(⁴/3 * π * 9³)
= ½(972π)
Volume of hemisphere = 486πcm³
Volume of the solid shape
= volume of cone + volume of the hemisphere.
==> 270πcm³ + 486πcm³
= 756πcm³
Answer/Step-by-step explanation:
Given:
C = right angle = 90°
BC = a = ?
AB = c = 12
AC = b = 9
Required:
a, <A, and <B
Solution:
✔️Find a using Pythagorean Theorem:
a = √(c² - b²)
a = √12² - 9²) = √63
a = 7.93725393 = 8 (nearest whole number)
✔️Find A by applying trigonometric ratio:
Thus,
Reference angle = A
Hypotenuse = 12
Adjacent = 9
Therefore,
m<A = 41° (nearest whole number)
✔️Find B:
m<B = 180 - (90 + 41) (sum of interior angles of triangle)
m<B = 49°