Surface area of a cuboid=2(b + bih hl)
3 Curved surface area of a cylinder = 2h
Surface area of a cube = 60%
2.
washed
find the
elted to
Total surface area of a cylinder = 2tr(v + h)
$ Curved surface area of a cone = trl
Total surface area of a right circular cone = trl + tur, i.e., tr (1 + r)
Surface area of a sphere of radius r = 4 r?
& Curved surface area of a hemisphere = 2162
9. Total surface area of a hemisphere = 37trº
10. Volume of a cuboid =lxbxh
11. Volume of a cube='
12. Volume of a cylinder Erh
V much
25
13. Volume of a cone =
27
14. Volume of a sphere of radiusr=r
10 cm
2
15. Volume of a hemisphere = 1
3
Here, letters 2, b, h, a,r, etc. have been used in their usual meani
Answers
Answer:
Two cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Sol. Volume of each cube = 64 cm3
∴ Total volume of the two cubes = 2 × 64 cm3
= 128 cm3
Let the edge of each cube = x
∴ x3 = 64 = 43
∴ x = 4 cm
Now, Length of the resulting cuboid l = 2x cm
Breadth of the resulting cuboid b = x cm
Height of the resulting cuboid h = x cm
∴ Surface area of the cuboid = 2 (lb + bh + hl) = 2[(2x . x) + (x . x) + (x . 2x)]
= 2[(2 × 4 × 4) + (4 × 4) + (4 × 2 × 4)] cm2
= 2 [32 + 16 + 32] cm2 = 2[80] cm2 = 160 cm2.
Q.2. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
Sol. For cylindrical part:
Radius (r) = 7 cm
Height (h) = 6 cm
∴ Curved surface area
= 2πrh
For hemispherical part:
Radius (r) = 7 cm
∴ Surface area = 2πr2
∴ Total surface area
= (264 + 308) cm2 = 572 cm2.
Q.3. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Sol. Here, r = 3.5 cm
∴ h = (15.5 – 3.5) cm = 12.0 cm
Surface area of the conical part
= πrl
Surface area of the hemispherical part
= 2πr2
∴ Total surface area of the toy
= πrl + 2πr2 = πr (l + 2r) cm2
∵ l2 = (12)2 + (3.5)2
Q.4. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
Sol. Side of the block = 7 cm
⇒ The greatest diameter of the hemisphere = 7 cm
Surface area of the solid
= [Total S.A. of the cubical block] + [S.A. of the hemisphere] – [Base area of the hemisphere]
= (6 × l2) + 2πr2 – πr2
Q.5. A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
Sol. Let ‘l’ be the side of the cube.
∴ The greatest diameter of the curved hemisphere = l
Q.6. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig.). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.
Sol. Radius of the hemispherical part
∴ Surface area of one hemispherical part = 2πr2
Q.7. A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respective