Surface Areas and Volumes: Introduction to Basic Solids

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Questions and Answers

What are some of the basic solids mentioned in the text?

cuboid, cone, cylinder, and sphere

Give an example of a common object that is a combination of a cylinder and hemisphere.

a truck with a container fitted on its back

What is the shape of a test tube?

a combination of a cylinder and a hemisphere

What kind of buildings or monuments are mentioned in the text?

<p>big and beautiful buildings or monuments made up of a combination of solids</p> Signup and view all the answers

What will be covered in this chapter according to the text?

<p>how to find surface areas and volumes of objects</p> Signup and view all the answers

How is the surface area of a combination of solids calculated?

<p>by considering each individual solid and summing up their surface areas</p> Signup and view all the answers

What is the total surface area of the block made of a cube and a hemisphere?

<p>163.86 cm^2</p> Signup and view all the answers

What are the dimensions of the wooden toy rocket that is in the shape of a cone mounted on a cylinder?

<p>Height of entire rocket: 26 cm, height of conical part: 6 cm, base diameter of conical portion: 5 cm, base diameter of cylindrical portion: 3 cm</p> Signup and view all the answers

What is the area of the rocket that is painted orange?

<p>37.7 cm^2</p> Signup and view all the answers

What is the area of the rocket that is painted yellow?

<p>88.5 cm^2</p> Signup and view all the answers

What is the base area of the hemisphere fixed on the block?

<p>13.86 cm^2</p> Signup and view all the answers

What is the slant height of the cone in the wooden toy rocket?

<p>13 cm</p> Signup and view all the answers

What is the inner surface area of the vessel described?

<p>$308 cm^2$</p> Signup and view all the answers

What is the total surface area of the toy described?

<p>$170.5 cm^2$</p> Signup and view all the answers

What is the greatest diameter the hemisphere can have on the cubical block described?

<p>7 cm</p> Signup and view all the answers

What is the surface area of the remaining solid after cutting out a hemispherical depression from a cubical wooden block?

<p>$108 cm^2$</p> Signup and view all the answers

What is the surface area of the medicine capsule described?

<p>$565.5 mm^2$</p> Signup and view all the answers

What is the area of the canvas used for making the tent?

<p>$107.04 m^2$</p> Signup and view all the answers

What is the area to be painted orange on the cone and cylinder?

<p>63.585 cm2</p> Signup and view all the answers

What is the area to be painted yellow on the cylinder?

<p>195.465 cm2</p> Signup and view all the answers

What is the total surface area of the bird-bath made by Mayank?

<p>33000 cm2</p> Signup and view all the answers

What is the total volume of the bird-bath made by Mayank?

<p>3.3 m2</p> Signup and view all the answers

What is the formula used to calculate the area to be painted orange on the cone and cylinder?

<p>CSA of the cone + base area of the cone - base area of the cylinder</p> Signup and view all the answers

How is the area to be painted yellow on the cylinder calculated?

<p>2πr'h' + π(r')^2</p> Signup and view all the answers

What is the total surface area of the remaining solid when a conical cavity is hollowed out from a solid cylinder with a height of 2.4 cm and diameter of 1.4 cm?

<p>37 cm^2</p> Signup and view all the answers

For a wooden article made by scooping out a hemisphere from each end of a solid cylinder with a height of 10 cm and base radius of 3.5 cm, what is the total surface area of the article?

<p>235 cm^2</p> Signup and view all the answers

In the shed described as a cuboid surmounted by a half cylinder with a base dimension of 7 m x 15 m and a cuboidal portion height of 8 m, what is the volume of air the shed can hold?

<p>748 m^3</p> Signup and view all the answers

How is the total surface area affected when a conical cavity of the same dimensions is hollowed out from a solid cylinder compared to the original solid?

<p>Decreases</p> Signup and view all the answers

Why is the volume of a solid formed by joining two basic solids the sum of the volumes of the constituents?

<p>Because no material is removed when joining the solids</p> Signup and view all the answers

What happens to the surface area when two basic solids are joined to form a new solid?

<p>Some part of the surface area disappears</p> Signup and view all the answers

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