A solid cylinder of height 30 cm and radius 10 cm , is melted and recast into cones of
Radius 3 cm and height 2 cm. Find the number of solid cones recast .
Answers
Answer:
Hi
Step-by-step explanation:
Answer:
Step-by-step explanation:
Height of the cylinder = 30 cm
Radius of the cylinder = 10 cm
Height of the cones = 2 cm
Radius of the cones = 3 cm
Number of solid cones recast
➣ Here we have to find the number of cones that can be recast from the solid cylinder.
➣ First we have to find the volume of the cylinder.
➣ Volume of a cylinder is given by,
Volume of a cylinder = π r² h
where r is the radius
h is the height
➣ Substitute the data,
Volume of the cylinder = 3.14 × 10² × 30
Volume of the cylinder = 9420 m³
➣ Hence volume of the cylinder is 9420 m³.
➣ Now finding the volume of one of the cones.
➣ Volume of a cone is given by,
Volume of a cone = 1/3 × π × r² × h
where r is the radius of the cone
h is the height of the cone
➣ Substitute the data,
Volume of the cone = 1/3 × 3.14 × 3² × 2
Volume of the cone = 18.84 m³
➣ Hence volume of each of the cone is 18.84 m³
➣ Now finding the number of cones that can be recast from it,
Number of cones = Volume of cylinder/Volume of cone
➣ Substitute the data,
Number of cones = 9420/18.84
Number of cones = 500
➣ Hence 500 cones can be made from the solid cylinder.
number of cones is 500