In this section of RS Aggarwal Class 9 Exercise 15C Solution (Volume and surface area of solids). All question are solved and described each term. Therefore all student can be understand easily.
RS Aggarwal and Veena Aggarwal Class 9 Ex. 15C
1: Find the curved surface area of a cone with base radius 5.25 cm and slant height 10 cm.
2: Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
3: A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make such caps.
4: The curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.
5: The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of whitewashing its curved surface at the rate of 12/m2.
6: A conical tent is 10 m high and the radius of its base is 24 m. Find the slant height of the tent. If the cost of 1 m2 canvas is Rs. 70, find the cost of canvas required to make the tent.
7: A bus stop is barricaded from the remaining part of the road by using 50 hollow cones made to recycled cardboard. Each one has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs. 25 per m2, what will be the cost of painting all these cones? (Use π =3.14 and √(1.04) =1.02
8: Find the volume, curved surface area and the total surface area of a cone having base radius 35 cm and height 12 cm.
9: Find the volume, curved surface area and the total surface area of a cone whose height is 6 cm and slant height 10 cm. (Take π =3.14)
10: A conical pit of diameter 3.5 m is 12 m deep. What is its capacity in kilolitre.
11: A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m .Find its volume. How much canvas cloth is required to just cover the heap? (Use π =3.14 )
12: A man uses a piece of canvas having an area of 551 m2, to make a conical tent of base radius 7 m. Assuming that all the stitching margins and wastage incurred while cutting, amount to approximately 1 m2, find the volume of the tent that can be made with it.
13: How many meters of cloth, 2.5 m wide, will be required to make a conical tent whose base radius is 7 m and height 24 m?
14: Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3 : 1. Show that their volumes are in the ratio 3 : 1.
15: A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8 : 5, Show that the radius and height of each has the ratio 3 : 4.
16: A right circular cone is 3.6 cm high and the radius of its base is 1.6 cm. It is melted and recast into a right circular cone having base radius 1.2 cm. Find its height.
17: A circus tent is cylindrical to a height of 3 m. And conical above it. If its diameter is 105 m and the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m wide to make the required tent.
18: An iron pillar consists of a conical portion 2.8 m high and 20 cm in diameter and a cone 42 cm high is surmounting it. Find the weight of the pillar, given that 1 cm3 of iron weights 7.5 g.
19: From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and base is removed. Find the volume of remaining solid. (Take π = 3.14)
20: Water flows at the rate of 10 meters per minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the surface is 40 cm and depth 24 cm?
21: A cloth having an area of 165 m2is shaped into the form of a conical tent of radius 5m. (i) How many students can sit in the tent if a student, on an average, occupies 5/7 m2 on the ground? (ii) Find the volume of the cone.
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