Mensuration Unit Exercise 7-10th Std Maths-Book Back Question And Answer
Question 1.
The barrel of a fountain-pen cylindrical in shape is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used for writing 330 words on an average. How many words can be written using a bottle of ink containing one-fifth of a litre?
Answer:
Question 2.
A hemispherical tank of radius 1.75 m is full of water. It is connected with a pipe which empties the tank at the rate of 7 litres per second. How much time will it take to empty the tank completely?
Answer:
Radius of the hemispherical tank = 1.75 m
Volume of the tank = 23πr3 cu.units
Time taken = 11229.177 = 1604.17 seconds = 26.74 minutes = 27 minutes (approximately)
Question 3.
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r units.
Answer:
Radius of a cone = Radius of a hemisphere = r unit
Height of a cone = r units
(height of the cone = radius of a hemisphere)
Maximum volume of the cone
Question 4.
An oil funnel of the tin sheet consists of a cylindrical portion 10 cm long attached to a frustum of a cone. If the total height is 22 cm, the diameter of the cylindrical portion by 8 cm and the diameter of the top of the funnel be 18 cm, then find the area of the tin sheet required to make the funnel.
Answer:
Total height of oil funnel = 22 cm
Height of the cylindrical portion = 10 cm
Height of the frustum (h) = 22 – 10 = 12 cm
Radius of the cylindrical portion = 4 cm
Radius of the bottom of the frustum = 4 cm
Top radius of the funnel (frustum) = 182 = 9 cm
Area of the tin sheet required = C.S.A of the frustum + C.S.A of the cylinder
= π (R + r) l + 2πrh sq. units.
= [π(9 + 4) 122+(9−4)2−−−−−−−−−−−√ + 2π × 4 × 10] cm2
= π [13 × 144+25−−−−−−−√ + 25 + 80] cm2
= 227 [13 × 13 + 80] cm2
= 227 [169 + 80] cm2
= 227 × 249 cm2
= 782.57 cm2
Area of sheet required to make the funnel = 782.57 cm2
Question 5.
Find the number of coins, 1.5 cm in diameter and 2 mm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
Answer:
Radius of the cylinder = 4.52 cm
Height of the cylinder = 10 cm
Volume of the cylinder = πr2h cu. units
Number of coins = 450
Question 6.
A hollow metallic cylinder whose external radius is 4.3 cm and internal radius is 1.1 cm and the whole length is 4 cm is melted and recast into a solid cylinder of 12 cm long. Find the diameter of a solid cylinder.
Answer:
External radius of the hollow cylinder R = 4.3 cm
Internal radius of the hollow cylinder r = 1.1 cm
Length of the cylinder (h) = 4 cm
Length of the solid cylinder (H) = 12 cm
Let the radius of the solid cylinder be “x”
Volume of the solid cylinder = Volume of the hollow cylinder
Diameter of the solid cylinder = 2 × 2.4 = 4.8 cm
Question 7.
The slant height of a frustum of a cone is 4 m and the perimeter of circular ends are 18 m and 16 m. Find the cost of painting its curved surface area at ₹ 100 per sq. m.
Answer:
Slant height of a frustum (l) = 4 m
Perimeter of the top part = 18 m
2πR = 18
Cost of painting = ₹ 100 × 68 = ₹ 6800
Question 8.
A hemispherical hollow bowl has material of volume cubic 436π3 cubic cm. Its external diameter is 14 cm. Find its thickness.
Answer:
External radius of a hemisphere (R) = 7 cm
Volume of a hemi-spherical bowl = 436π3 cm3
Internal radius = 5 cm
Thickness of the hemisphere = (7 – 5) cm = 2 cm
Question 9.
The volume of a cone is 100557 cu. cm. The area of its base is 20117 sq. cm. Find the slant height of the cone.
Answer:
Area of the base of a cone = 20117 sq. cm
Question 10.
A metallic sheet in the form of a sector of a circle of radius 21 cm has a central angle of 216°. The sector is made into a cone by bringing the bounding radii together. Find the volume of the cone formed.
Answer:
Radius of a cone (r) = 21 cm
Central angle (θ) = 216°
Let “R” be the radius of a cone
Circumference of the base of a cone = arc length of the sector
2πR = θ360×2πr
