Question

What is the combined volume of the figures below rounded to the nearest whole number?​

Answer 1

Hello !

Answer:

`\boxed{\sf \to V\approx 170cm^3}`

Explanation:

• Sphere

To find the volume of a sphere with its radius, we will apply the following formula:

`\sf V_(sphere)=(4*\pi* r^3)/(3)`

Where r is the radius of the sphere.

Given :

• r = 3cm

Let's substitute our value into the formula:

`\sf V_(sphere)=(4*\pi* 3^3)/(3)\\V_(sphere)=36\pi\\\boxed{\sf V_(sphere)\approx 113.1cm^3}`

• Cone

To find the volume of a cone with the radius of its base and its height, we will apply the following formula:

`\sf V{cone} = (\pi * r^2 * h)/(3)`

Where r is the radius of its base and h is its height.

Given :

• r = 3cm
• h = 6 cm

Let's substitute our values into the formula:

`\sf V_(cone)=(\pi* 3^2 * 6)/(3)\\V_(cone)=18\pi\\\boxed{\sf V_(cone) \approx 56.55cm^3}`

• Combined volume

The combined volume of the two figures is the sum of the two volumes.

`\sf V = V_(cone) + V_(sphere)\\V\approx 113.1+56.55\\V\approx169.65cm^3\\\boxed{\sf V\approx170cm^3}`

Have a nice day ;)