Question

A cone is cut into a cube as shown below. If the cone has a diameter of

Answer 1

Answer:

184.43in².

Step-by-step explanation:

Total surface area of the solid = volume of the cube - the volume of the cone

For the CUBE;

Volume of the cube = L³ where L is the length of one side of the cube.

Since a cone of diameter of 6in is cut into a cube, then the length of the cube will be 6in.

Volume of the cube = 6³ = 216in³

For the CONE;

Volume of the cone = 1/3 πr²h

r is the radius of the cone = diameter/2

r = 6/2 = 3in

slant height l = 4.5in

the height h of the cone will be derived using the Pythagoras theorem.

l² = h²+r²

4.5² = h²+3²

h² = 4.5²-3²

h² = 11.25

h=√11.25

h = 3.35in

Volume of the cone = 1/3 × π × 3²× 3.35

= 31.57in³

Total surface area of the solid = 216in³-31.57in³

= 184.43in²