Question

Q 1 A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is:

(A) 4.2 cm (B) 2.1 cm (C) 2.4 cm (D) 1.6 cm

Q2 In a right circular cone, height, radius and slant height do not always be sides of a right triangle.

Solution:


Q3 If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.

Solution


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Answer 1

Answer:

Step-by-step explanation:

For the cone,

radius, r = 2.1cm

height, h = 8.4 cm

For the sphere,

radius = R

Cone is melted and recast into sphere.

So, Volume of sphere = Volume of cone

∴ 4/3 π R³ = 1/3 π r² h

∴4 R³ = r² h

∴4 R³ = 2.1² * 8.4

∴R³ = 2.1² * 8.4 / 4

∴R³ =  2.1² * 2.1

∴R³ = 2.1³

∴R = 2.1 cm

Answer 2

Step-by-step explanation:

Ques.1 ...2.1cm

Ques.2...Its base is a circle with centre O and radius OB. The length OA is the height of the cone and the length AB is called its slant height. Hence, in a right circule cone, height radius and slant height do not always be side of a right triangle.

Ques.3.....Hence, the given statement “If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved” is true.

(copied from Googl*)