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Practice each question, then open the answer or worked solution.
Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr2.
False
Explanation:
When two hemispheres are joined together along their bases, a sphere of same base radius is formed.
Curved Surface Area of a sphere = 4πr2.
A solid cylinder of radius r and height h is placed over another cylinder of the same height and radius. The total surface area of the shape so formed is 4πrh + 4πr2.
False
Explanation:
According to the question,
When one cylinder is placed over another, the base of first cylinder and top of another cylinder will not be covered in total surface area.
We know that,
Total surface area of cylinder = 2πrh + 2πr2h, where r = base radius and h = height
Total surface area of shape formed = 2(Total surface of single cylinder) – 2(Area of base of cylinder)
= 2(2πrh + 2πr2) – 2(πr2)
= 4πrh + 2πr2
A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is πr[√(r2 + h2 +3r + 2h].
False
Explanation:
When a solid cone is placed over a solid cylinder of same base radius, the base of cone and top of the cylinder will not be covered in total surface area.
Since the height of cone and cylinder is same,
We get,
Total surface area of cone = πrl + πr2, where r = base radius and l = slant height
Total surface area of shape formed = Total surface area of cone + Total Surface area of cylinder – 2(Area of base)
Total surface area of cylinder = 2πrh + 2πr2h, where r = base radius and h = height
= πr(r + l) + (2πrh + 2πr2) – 2(πr2)
= πr2 + πrl + 2πrh + 2πr2 – 2πr2
= πr(r + l + h)
A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is 4/3πa3.
False
Explanation:
Let the radius of sphere = r
When a solid ball is exactly fitted inside the cubical box of side a,
We get,
Diameter of ball = Edge length of cube
2r = a
Radius, r = a/2
We also know that,
Volume of sphere = 4/3πr3
Volume of ball = 4/3π(a/2)3 = 4/3π(a3/8) = 1/6πa3