Question

Work out the volume of the solid shape Give your answers in terms of pi please

Answer 1

*The complete question is in the picture attached below.

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