Question

Can someone help me with this geometry question? I will provide the rest of the question.Match each figure with their surface area rounded to the nearest square unit.

Answer 1

On the first figure, given that:

Radius of cone, r = 10 units

Height of cone, h = 10 units

The formula to find the surface area of cone is

`SA=\pi r(r+\sqrt[]{h^2+r^2})`

Plug the values into the formula.

`\begin{gathered} SA=\pi\cdot10(10+\sqrt[]{10^2+10^2}) \\ =10\pi(10+10\sqrt[]{2}) \\ \approx758 \end{gathered}`

The surface area is 758 square units.

On the second figure, given that:

Radius of cone, r = 12 units

Height of cone, h = 8 units

The formula to find the surface area of cone is

`SA=\pi r(r+\sqrt[]{h^2+r^2})`

Plug the values into the formula.

`\begin{gathered} SA=\pi\cdot12(12+\sqrt[]{8^2+12^2}) \\ =12\pi(12+\sqrt[]{208}) \\ \approx996 \end{gathered}`

The surface area is 996 square units.

On the third figure, given that:

Radius of cone, r = 16/2 units = 8 units

Height of cone, h = 15 units

The formula to find the surface area of cone is

`SA=\pi r(r+\sqrt[]{h^2+r^2})`

Plug the values into the formula.

`\begin{gathered} SA=\pi\cdot8(8+\sqrt[]{15^2+8^2}) \\ =8\pi(8+\sqrt[]{289}) \\ \approx628 \end{gathered}`

The surface area is 628 square units.

On the fourth figure, given that:

Radius of cone, r = 12/2 units = 6 units

Height of cone, h = 21 units

The formula to find the surface area of cone is

`SA=\pi r(r+\sqrt[]{h^2+r^2})`

Plug the values into the formula.

`\begin{gathered} SA=\pi\cdot6(6+\sqrt[]{21^2+6^2}) \\ =6\pi(6+\sqrt[]{477}) \\ \approx525 \end{gathered}`

The surface area is 525 square units.