SELINA CHAPTER 20 SOLUTIONS_ EX 20B , 20E , 20F , 20G _MENSURATION
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EXERCISE 20(B)
10. A solid cone of height 8 cm and base radius
6 cm is melted and recast into identical cones,
each of height 2 cm and diameter 1 cm. Find
the number of cones formed.
11. The total surface area of a right circular cone of slant height 13 cm is 90 pi cm2.
Calculate :
i) its radius in cm.
(ii) its volume in cm3. [Take = 3-14] .
13. A vessel, in the form of an inverted cone, is
filled with water to the brim. Its height is
32 cm and diameter of the base is 25-2 cm.
Six equal solid cones are dropped in it, s
that they are fully submerged. As a result,
one-fourth of water in the original cone
overflows. What is the volume of each of the
solid cones submerged ?
'14 The volume of a conical tent is 1232 M3 and
the area of the base floor is 154 m2. Calculate
the
(i) radius of the floor,
(ii) height of the tent,
(iii) length of the canvas required to cover this conical tent if its width is 2 m.
EXERCISE 20 D
10. A solid metallic cone, with radius
6 cm and height 10 cm, is made of
some heavy metal A. In order to
reduce its weight, a conical hole is
made in the cone as shown and it
is completely filled with a lighter metal. THE
conical hole has a diameter of 6 cm and depth
cm. Calculate the ratio of the volume of metal
A to THE volume of the metal B in the solid.
EXERCISE 20(E)
3. From a rectangular solid of metal 42 cm by
30 cm by 20 cm, a conical cavity of diameter
14 cm and depth 24 cm is drilled out. Find :
(1) the surface area of remaining solid,
(ii) the volume of remaining solid,
(iii) the weight of the material drilled out
weighs 7 gm per cm^3.
EXERCISE 20(F)
4. A circus tent is cylindrical to a height of 8 m
surmounted by a conical part. If total height
of the tent is 13 m and the diameter of its base
is 24 m; calculate
i) total surface area of the tent,8.
(ii) area of canvas, required to make this tent
allowing 10% of the canvas used for folds
and stitching.
7. A wooden toy is in the shape of
a cone mounted on a cylinder as
shown alongside.
If the height of the cone is 24 cm,
the total height of the toy is 60 cm
and the radius of the base of the
cone = twice the radius of the base of the cylinder
= 10 cm: find the total surface area of the toy.
[Take pi= 3-14]
13. An open cylindrical vessel of internal diameter
cm and height 8 cm stands on a horizontal
table. Inside this is placed a solid metallic right
circular cone. the diameter of whose base is
cm and height 8 cm. Find the volume of
water required to fill the vessel.
If this cone is replaced by another cone,
whose height is 1 3/4 cm and the radius of whose
base is 2 cm, find the drop in the water level.
EXERCISE 20(F)
7. An iron pole consisting of a cylindrical portion
110 cm high and of base diameter 12 cm is
surmounted by a cone 9 cm high. Find
the mass of the pole, given that 1 cm^3 of iron
has 8 gm of mass (approx). (Take pi=355/113)
10. A cylindrical water tank of diameter 2.8 m and
height 4.2 m is being fed by a pipe of
diameter 7 cm through which water flows at
the rate of 4 m/s . Calculate, in minutes, the
time it takes to fill the tank.
11. Water flows, at 9 km per hour, through a
cylindrical pipe of cross-sectional area 25 cm^2.
If this water is collected into a rectangular
cistern of dimensions 7.5 m by 5 m by 4 m;
calculate the rise in level in the cistern in
1 hour 15 minutes.
15. An exhibition tent is in the form of a cylinder surmounted by a cone.
The height of the tent
surmounted by a cone. The height of the tent
above the ground is 85 m and height of the
cylindrical part is 50 m. If the diameter of the
base is 168 m, find the quantity of canvas
base is 168 m, find the quantity of canvas
required to make the tent. Allow 20% extra for
fold and for stitching. Give your answer to the
nearest m^2. [2001]
20. A conical tent is to accomodate 77 persons.
Each person must have 16m^3 of air to
breathe. Given the radius of th ent as 7 m,
is total find the height of the tent and also its curved
surface area.