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Given,
The Volume (V) of each cube is = 64 cm
3
This implies that a
3
= 64 cm
3
∴ a = 4 cm
Now, the side of the cube = a = 4 cm
Also, the length and breadth of the resulting cuboid will be 4 cm each, while its height will be 8 cm.
So, the surface area of the cuboid = 2(lb+bh+lh)
= 2(8×4+4×4+4×8) cm
2
= 2(32+16+32) cm
2
= (2×80) cm
2
= 160 cm
2
Now, the given parameters are:
The diameter of the hemisphere = D = 14 cm
The radius of the hemisphere = r = 7 cm
Also, the height of the cylinder = h = (13-7) = 6 cm
And the radius of the hollow hemisphere = 7 cm
Now, the inner surface area of the vessel = CSA of the cylindrical part + CSA of the hemispherical part
(2πrh+2πr
2
) cm
2
= 2πr(h+r) cm
2
2×(22/7)×7(6+7) cm
2
= 572 cm
2
Given that the radius of the cone and the hemisphere (r) = 3.5 cm or 7/2 cm
The total height of the toy is given as 15.5 cm.
So, the height of the cone (h) = 15.5-3.5 = 12 cm
∴ The curved surface area of the cone = πrl
(22/7)×(7/2)×(25/2) = 275/2 cm
2
Also, the curved surface area of the hemisphere = 2πr
2
2×(22/7)×(7/2)
2
= 77 cm
2
Now, the Total surface area of the toy = CSA of the cone + CSA of the hemisphere
= (275/2)+77 cm
2
= (275+154)/2 cm
2
= 429/2 cm
2
= 214.5cm
2
So, the total surface area (TSA) of the toy is 214.5cm
2
Here, the diameter of the capsule = 5 mm
∴ Radius = 5/2 = 2.5 mm
Now, the length of the capsule = 14 mm
So, the length of the cylinder = 14-(2.5+2.5) = 9 mm
∴ The surface area of a hemisphere = 2πr
2
= 2×(22/7)×2.5×2.5
= 275/7 mm
2
Now, the surface area of the cylinder = 2πrh
= 2×(22/7)×2.5×9
(22/7)×45 = 990/7 mm
2
Thus, the required surface area of the medicine capsule will be
= 2×surface area of hemisphere + surface area of the cylinder
= (2×275/7) × 990/7
= (550/7) + (990/7) = 1540/7 = 220 mm
2
From the question, we know that
Diameter = 4 m
The slant height of the cone (l) = 2.8 m
Radius of the cone (r) = Radius of cylinder = 4/2 = 2 m
Height of the cylinder (h) = 2.1 m
So, the required surface area of the tent = surface area of the cone + surface area of the cylinder
= πrl+2πrh
= πr(l+2h)
= (22/7)×2(2.8+2×2.1)
= (44/7)(2.8+4.2)
= (44/7)×7 = 44 m
2
∴ The cost of the canvas of the tent at the rate of ₹500 per m
2
will be
= Surface area × cost per m
2
44×500 = ₹22000
So, Rs. 22000 will be the total cost of the canvas.
From the question, we know the following:
The diameter of the cylinder = diameter of conical cavity = 1.4 cm
So, the radius of the cylinder = radius of the conical cavity = 1.4/2 = 0.7
Also, the height of the cylinder = height of the conical cavity = 2.4 cm
Now, the TSA of the remaining solid = surface area of conical cavity + TSA of the cylinder
= πrl+(2πrh+πr
2
)
= πr(l+2h+r)
= (22/7)× 0.7(2.5+4.8+0.7)
= 2.2×8 = 17.6 cm
2
So, the total surface area of the remaining solid is 17.6 cm
2
