Volume & Surface Areas Questions and Answers

Q: A solid with a vertex and a base that is formed by a simple closed curve is a

A cone has a single apex and a base bounded by a simple closed curve - in the familiar right circular cone, that curve is a circle.The distinction from a pyramid is exactly the base: a pyramid's base is a polygon, made of straight edges, while a cone's is a smooth closed curve.A triangle is a plane figure, not a solid, and a dice is a cube with no apex at all.

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171.

A solid with a vertex and a base that is formed by a simple closed curve is a

A.Triangle
B.Cone
C.Pyramid
D.Dice

Answer: B

A cone has a single apex and a base bounded by a simple closed curve - in the familiar right circular cone, that curve is a circle.

The distinction from a pyramid is exactly the base: a pyramid's base is a polygon, made of straight edges, while a cone's is a smooth closed curve.

A triangle is a plane figure, not a solid, and a dice is a cube with no apex at all.

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172.

The length, breadth and height of a room are 12 m, 10 m and 9 m respectively. Find the combined area of its four walls and its ceiling.

A.636 m²
B.516 m²
C.800 m²
D.456m²

Answer: B

The four walls form a band of height 9 m around the floor's perimeter, and the ceiling is a rectangle the same size as the floor.

\[ \text{four walls} = 2(l + b)h = 2(12 + 10) \times 9 = 2 \times 22 \times 9 = 396 \text{ m}^{2} \]

\[ \text{ceiling} = l \times b = 12 \times 10 = 120 \text{ m}^{2} \]

\[ \text{total} = 396 + 120 = 516 \text{ m}^{2} \]

The floor is excluded, so this is not the full surface area of the cuboid - that would be \( 396 + 240 = 636 \) m², which is offered as the first distractor.

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173.

The plastic paint in a Asian paint container is sufficient to paint an area equal to 93.75m². How many blocks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container

A.100
B.800
C.940
D.1000

Answer: D

Total surface area of one block = 2(lb + bh + lh)
= [2(22.5 ×10 + 10 × 7.5 + 22.5 × 7.5)] cm
= 2(225 + 75 + 168.75) cm²
= (2 × 468.75) cm²
= 937.5 cm²
Let n blocks can be painted out by the paint of the container.
Area of n bricks = (n ×937.5) cm² = 937.5n cm²
Area that can be painted by the paint of the container = 93.75 m2= 937500 cm²
937500 = 937.5n
n = 1000
Therefore, 100 blocks can be painted out by the paint of the container

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174.

The curved surface area of a cone is 308 cm² and its slant height is 14 cm. Which of the following statements is true?

A.Radius of the cone is 14 cm
B.total surface area is 462 cm²
C.Height of the cone is \( 147^{2} \) cm
D.None of the above

Answer: B

Start from the curved surface area to find the radius, taking \( \pi = \tfrac{22}{7} \).

\[ \pi r l = 308 \quad\Longrightarrow\quad \frac{22}{7} \times r \times 14 = 308 \]

\[ 44r = 308 \quad\Longrightarrow\quad r = 7 \text{ cm} \]

Now the total surface area adds the base:

\[ \text{TSA} = \pi r(l + r) = \frac{22}{7} \times 7 \times (14 + 7) = 22 \times 21 = 462 \text{ cm}^{2} \]

So the true statement is that the total surface area is 462 cm².

Checking the others: the radius is 7 cm, not 14 - 14 cm is the slant height. The height is \( \sqrt{l^{2} - r^{2}} = \sqrt{196 - 49} = \sqrt{147} \approx 12.1 \) cm, which is the square root of 147, not its square.

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