Volume of prisms, pyramids, cones, cylinders, spheres

Front

What is the formula for the volume of a cylinder?

Back

Volume = πr²h, where r is the radius and h is the height.

Front

How do you calculate the volume of a cone?

Back

Volume = (1/3)πr²h, where r is the radius of the base and h is the height.

Front

What is the formula for the volume of a sphere?

Back

Volume = (4/3)πr³, where r is the radius.

Front

If the height of a cone is twice the radius, how does this affect its volume?

Back

The volume increases as the height increases, specifically, V = (2/3)πr²(2r) = (4/3)πr³.

Front

What is the volume of a cylinder with a radius of 5 cm and a height of 10 cm?

Back

Volume = π(5)²(10) = 250π cm³.

Front

How do you find the volume of a pyramid?

Back

Volume = (1/3)Bh, where B is the area of the base and h is the height.

Front

What is the relationship between the radius and the volume of a sphere?

Back

The volume of a sphere increases with the cube of the radius (V ∝ r³).

Front

Calculate the volume of a cone with a base area of 25π and height of 10 cm.

Back

Volume = (1/3)(25π)(10) = 250π cm³.

Front

What is the volume of a sphere with a radius of 6 ft?

Back

Volume = (4/3)π(6)³ = 904.32 ft³.

Front

How do you find the volume of a composite figure made of prisms and pyramids?

Back

Calculate the volume of each shape separately and then sum them up.