Contents
Andhra Pradesh SSC Class 10 Solutions For Maths – Mensuration (English Medium)
These Solutions are part of AP SSC Class 10 Solutions for Maths. In this article, we have provided Andhra Pradesh SSC Class 10 Solutions For Maths Chapter 10 Mensuration
Exercise 10.1:
Question 1:
A joker’s cap is in the form of right circular cone whose base radius is 7cm and height is 24 Find the area of the sheet required to make 10 such caps.
Solution :
AP SSC 10th Class Textbook Solutions
Question 2:
A sports company was ordered to prepare 100 paper cylinders for packing shuttle cocks. The required dimensions of the cylinder are 35 cm length /height and its radius is 7 cm. Find the required area of thick paper sheet needed to make 100 cylinders?
Solution :
Question 3:
Find the volume of right circular cone with radius 6 cm. and height 7 cm.
Solution :
Question 4:
The lateral surface area of a cylinder is equal to the curved surface area of a cone. If their bases be the same, find the ratio of the height of the cylinder to the slant height of the cone.
Solution :
Question 5:
A self help group wants to manufacture joker’s caps of3cm. radius and 4 cm. height. If the available paper sheet is 1000 cm2 , then how many caps can be manufactured from that paper sheet?
Solution :
Question 6:
A cylinder and cone have bases of equal radii and are of equal heights. Show that their volumes are in the ratio of 3: 1.
Solution :
Question 7:
The shape of solid iron rod is a cylinderical. Its height is 11 cm. and base diameter is 7cm. Then find the total volume of 50 such rods?
Solution :
Question 8:
A heap of rice is in the form of a cone of diameter 12 m. and height 8m. Find its volume? How much canvas cloth is required to cover the heap ? (Use π = 3.14)
Solution :
Question 9:
The curved surface area of a cone is 4070 cm2 and its diameter is 70 cm. What is its slant height?
Solution :
The curved surface area=πrl
4070=110 × l
Slant height(l)=37cm
Exercise 10.2:
Question 1:
A toy is in the form of a cone mounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm respectively. Determine the surface area of the toy. [use π = 3.14]
Solution :
Question 2:
A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end. The radius of the common base is 8 cm. and the heights of the cylindrical and conical portions are 10 cm and 6 cm respectively. Find the total surface area of the solid. [use π = 3.14]
Solution :
Question 3:
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the capsule is 14 mm. and the width is 5 mm. Find its surface area.
Solution :
Question 4:
Two cubes each of volume 64 cm3 are joined end to end together. Find the surface area Of the resulting cuboid.
Solution :
Question 5:
A storage tank consists of a circular cylinder with a hemisphere stuck on either end. If the external diameter of the cylinder be 1.4 m. and its length be 8 m. find the cost of painting it on the outside at rate of D20 per m2.
Solution :
Question 6:
A sphere, a cylinder and a cone have the same radius and same height. Find the ratio of their volumes. [Hint : Diameter of the sphere is equal to the heights of the cylinder and the cone.]
Solution :
Question 7:
A hemisphere is cut out from one face of a cubical wooden block such that the diameter of the hemisphere is equal to the length of the cube. Determine the surface area of the remaining solid.
Solution :
Question 8:
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is 10 cm. and its radius of the base is of 3.5 cm, find the total surface area of the article.
Solution :
Exercise 10.3:
Question 1:
An iron pillar consists of a cylindrical portion of 2.8 m. height and 20 cm. in diameter and A cone of 42 cm. height surmounting it. Find the weight of the pillar if 1 cm3 of iron weighs 7.5 g.
Solution :
Question 2:
A toy is made in the form of hemisphere surmounted by a right cone whose circular base is joined with the plane surface of the hemisphere. The radius of the base of the cone is 7 cm. and its volume is \(\frac{3}{2}\) of the hemisphere. Calculate the height of the cone and the surface area of the toy correct to 2 places of decimal (Take π = 3\(\frac{1}{7}\)).
Solution :
Question 3:
Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 7 cm.
Solution :
Question 4:
A cylinderical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of right circular cone mounted on a hemisphere is immersed into the tub. The radius of the hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm. Find the volume of water left in the tub (Take π = 3\(\frac{1}{7}\)).
Solution :
Question 5:
In the adjacent figure, the height of a solid cylinder is 10 cm and diameter is 7 cm. Two equal conical holes of radius 3 cm and height 4 cm are cut off as shown the figure. Find the volume of the remaining solid.
Solution :
Question 6:
Spherical Marbles of diameter 1.4 cm. are dropped into a cylindrical beaker of diameter 7 cm. , which contains some water. Find the number of marbles that should be dropped in to the beaker, so that water level rises by 5.6 cm.
Solution :
Question 7:
A pen stand is made of wood in the shape of cuboid with three conical depressions to hold the pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depression is 0.5 cm and the depth is 1.4cm. Find the volume of wood in the entire stand.
Solution :
Exercise 10.4:
Question 1:
A metallic sphere of radius 4.2 cm. is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
Solution :
Question 2:
Three metallic spheres of radii 6 cm., 8 cm. and 10 cm. respectively are melted together to form a single solid sphere. Find the radius of the resulting sphere.
Solution :
Question 3:
A 20 m deep well of diameter 7 m. is dug and the earth got by digging is evenly spread out to form a rectangular platform of base 22 m × 14 m. Find the height of the platform.
Solution :
Question 4:
A well of diameter 14 m. is dug 15 m. deep. The earth taken out of it has been spread evenly to form circular embankment of width 7 m. Find the height of the embankment.
Solution :
Question 5:
A container shaped like a right circular cylinder having diameter 12 cm. and height 15 cm. is full of ice cream. The ice cream is to be filled into cones of height 12 cm. and diameter 6 cm., having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Solution :
Question 6:
How many silver coins, 1.75 cm. in diameter and thickness 2 mm., need to be melted to form a cuboid of dimensions 5.5 cm. × 10 cm. × 3.5 cm.?
Solution :
Question 7:
A vessel is in the form of an inverted cone. Its height is 8 cm. and the radius of its top is 5 It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, \(\frac{1}{4}\) of the water flows out. Find the number of lead shots dropped into the vessel.
Solution :
Question 8:
A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter 4\(\frac{2}{3}\) cm and height 3cm. Find the number of cones so formed.
Solution :
Hope given Andhra Pradesh SSC Class 10 Solutions For Maths chapter 10 Mensuration are helpful to complete your math homework.
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