A cone is cut off from a cuboidal block of dimensions 15 cm 10 cm x 5 cm. The diameter and height of the
430
cone are 5 cm and 7 cm respectively. Find the total volume of the remaining block.
Answers
The total volume of the remaining block is 704.17 cm³ .
Step-by-step explanation:
The dimensions of the cuboidal block:
Length, l = 15 cm
Breadth, b = 10 cm
Height, h = 5 cm
∴ The volume of the cuboidal block = l * b * h = 15 * 10 * 5 = 750 cm³
The dimensions of the cone:
Diameter, d = 5 cm
∴ Radius, r = d/2 = 5/2 = 2.5 cm
Height, h = 7 cm
∴ The volume of the cone cut out from the block,
= 1/3 * πr²h
= (1/3) * (22/7) * (2.5)² * 7
= 45.83 cm³
Thus,
The total volume of the remaining block is given by,
= [volume of the cuboidal block] – [volume of the cone cut out from the block]
= 750 – 45.83
= 704.17 cm³
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