What is the exact volume of the figure?

810π cm³  

Step-by-step explanation:

The figure is a hemisphere cone.

We can calculate the volumes of the two portions separately.

(a) Volume of the cone

         Diameter of hemisphere = 18 cm

            Radius of hemisphere  =  9 cm

Height of cone + hemisphere  = 21 cm

          h             +          9           = 21     Subtract 9 from each side

          h                                      = 12 cm

The formula for the volume of a cone is

V₁ = ⅓πr²h

V₁ = ⅓π × 9² × 12

   = ⅓π × 81 × 12

   = 324π cm³

(b) Volume of hemisphere

The formula for the volume of a sphere is

V = ⁴/₃πr³

So, the formula for the volume of a hemisphere is

V = ⅔πr³

V₂ = ⅔π ×   9³

V₂ = ⅔π × 729

  = 486π cm³

(c) Volume of hemisphere cone

V =     V₁   +   V₂

   = 324π + 486π

   = 810π cm³  

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation:

c: y > - 1/6x + 1

step-by-step explanation:

dashed line - meaning this < or > also not equal

solid line - meaning this < or > also equal

your answer is c because y > means up & it's shaded up, but y < means down

hope this ! : )