One specific toy is in the shape of a cone mounted on a cylinder. The total height of the toy is 110 mm and the height of its conical part is 77 mm. The diameters of the base of the conical part is 72 mm and that of the cylindrical part is 40 mm.
(iii) How much of the wood have been used in making the toy ? (a) 56824 pi mm3 (b) 46464 pi mm3 (c) 84424 pi mm3 (d) 64684 pi mm3
Answers
One specific toy is in the shape of a cone mounted on a cylinder. The total height of the toy is 110 mm and the height of its conical part is 77 mm. The diameters of the base of the conical part is 72 mm and that of the cylindrical part is 40 mm.
(iii) How much of the wood have been used in making the toy ? (a) 56824 pi mm3 (b) 46464 pi mm3 (c) 84424 pi mm3 (d) 64684 pi mm3
Given :-
- Total height of the toy = 110mm .
- Height of conical part = 77mm.
- Diameter of base of conical part = 72mm.
- Diameter of cylindrical part = 40mm.
To Find :-
- How much of the wood have been used in making the toy ?
Solution :-
we know that,
- Volume of cylinder = π * (radius)² * height .
- Volume of cone = (1/3) * π * (radius)² * height .
→ Height of cylinder = Total height of toy - Height of conical part = 110 - 77 = 33mm.
so,
→ Total wood used = Volume of conical part + Volume of cylinder
→ Total wood used = (1/3)π(36)²*77 + π(20)²*33
→ Total wood used = π(12*36*77 + 400*33)
→ Total wood used = π(33264 + 13200)
→ Total wood used = 46464π mm³. (Option B) (Ans.)
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