1A combined solid is a cone joined to a cylinder. Its total volume is 1050 cm³ and the volume of the cylindrical part is 748 cm³. Find the volume of the conical part.
2A cone is joined to one end of a cylinder. The curved surface of the conical part is 252 cm², the curved surface of the cylindrical part is 272 cm² and the area of the circular end is 154 cm². Find the total surface area.
3A square based pyramid stands on a square based prism. The area of the base is 36 cm² and the volume of the prism is 144 cm³. The prism is h high and the whole solid is 2h high. Find the volume of the pyramid.
4A hemisphere of radius r sits on a cone whose slant height is 2r. The curved surface of the conical part is 308 cm². Find the curved surface area of the hemispherical part.
5A solid is a cylinder of diameter 40 cm and length 70 cm, with a cone 10 cm high at one end. Find its volume.
6A square based pyramid stands on a square based prism of base side 12 cm and height 6 cm. The whole solid is 15 cm tall. Find its volume.
7A hemisphere sits on a cone. The cone is 42 cm high and the whole solid is 56 cm tall. Find its volume.
8Two cones share a circular base of diameter 14 cm. One cone is 6 cm high and the other is 9 cm high. Find the volume.
9In a crystal, the middle square has side 2.5 cm. The total height of the object is 4.5 cm, and the upper and lower pyramids have equal heights. Find the total surface area and volume of the crystal.
10A cylinder of diameter 6 cm and length 116 cm has a cone at one end, making the solid 120 cm long. Find its total surface area.
11A cylinder of diameter 14 cm and length 32 cm has a cone of slant height 25 cm at one end. Find the total surface area.
12A hemisphere is joined to a cone of height 24 cm. The solid is 31 cm long from the cone's tip to the far side of the hemisphere. Find the total surface area.
13A hemisphere is joined to a cone of height 48 cm and slant height 50 cm. Find the total surface area.
14A pyramid 8 cm high stands on a square prism of base side 30 cm. The whole solid is 28 cm tall. Find the total surface area.
15A pyramid stands on a square prism of base side 6 cm and height 6 cm. The whole solid is 29 cm tall. Find the total surface area.
16A toy has conical and hemispherical parts of radius 14 cm. Find its total surface area if its total height is 49 cm.
17A pyramid of height 12 cm is placed on top of a solid square based cuboid. The base area of the cuboid is 100 cm² and its height is 10 cm. Find the total volume and the total surface area of the combined solid.
18A pyramid with vertical height 8 cm is placed on top of a solid cube of side 12 cm. Find the total volume of the combined solid.
19A solid is made of a cone and a cylinder. The base area of the cylinder is 100 cm² and its height is 3 cm. Find the total height of the solid if its total volume is 600 cm³.
20The upper part of a solid is a pyramid with slant height 5 cm. The lower part is a square based prism with base side 8 cm. If the volume of the solid is 448 cm³, find the height of the prism shaped portion.
21A square based pyramid is placed on top of a tower. The tower and the pyramid are each 6 ft high, and the base of the tower is 1 ft square. Find the lateral surface area of the pyramid shaped portion, and the total surface area of the tower that can be painted.
22Ram received a spinning top from his father on his sixth birthday. Its lower part is conical and its upper part is hemispherical. The total height is 5 cm and the diameter of the hemisphere is 3.5 cm. Ram plans to colour it. Find the area of the surface that can be coloured.
23Are the total surface area and the lateral surface area equal for all types of combined solid objects?
24Show that the total surface area of a cylinder with a hemisphere on one end is \( 2\pi r h + 3\pi r^2 \).
25A separate cone and hemisphere, each of radius 7 cm, are joined. By how much does the total surface area go down, and what happens to the volume?