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I found this year old question on a blog.
Anthony controls Wild Evocation. At the beginning of his upkeep, he triggers and begins resolving Wild Evocation's triggered ability, revealing Disaster Radius. Disaster Radius has a mandatory additional cost of revealing a creature card from your hand.
Is Anthony required to pay the mandatory additional cost of revealing a creature card from his hand if he is able?
If Anthony can pay the cost, and it isn't a mana cost, and it doesn't involve cards with a specific quality in a hidden zone, it must be paid if able. If it is a mana cost and there is enough mana in his mana pool to pay it it must be paid, otherwise he has the option to activate mana abilities to pay for. If the cost involves cards with a specific quality in a hidden zone Anthony may choose to pay for it if he wants to, but is not required to. If the cards mandatory additional costs can't be paid, or he chooses not to pay an additional mana cost the card is uncast and stays in his hand.
117.8c. If an effect instructs a player to cast a spell “if able,” and that spell has a mandatory additional cost that includes actions involving cards with a stated quality in a hidden zone, the player isn’t required to cast that spell, even if those cards are present in that zone.
From the Gatherer Rulings:
If casting the revealed card involves paying a mandatory additional cost (such as the one Fling has), the player casting that card must pay that cost if able. If he or she can't, the card remains uncast in his or her hand. If the mandatory additional cost includes a mana payment, the situation is more complex. If the player has enough mana in his or her mana pool to pay the cost, that player must do so. If the player can't possibly pay the cost, the card remains uncast in his or her hand. However, if the player has the means to produce enough mana to pay the cost, then he or she has a choice: The player may cast the card, produce mana, and pay the cost. Or the player may choose to activate no mana abilities, thus making the card impossible to cast because the additional mana can't be paid.
To summarize the other answers and comments:
Under current rules, you are not required to reveal a creature card from your hand, even if you actually have one. However, if you do not, you will not be able to cast Disaster Radius.
The relevant rule is 117.8c, which reads:
117.8c If an effect instructs a player to cast a spell “if able,” and that spell has a mandatory additional cost that includes actions involving cards with a stated quality in a hidden zone, the player isn’t required to cast that spell, even if those cards are present in that zone.
"Reveal a creature card from your hand" is an action ("reveal") involving cards with a stated quality ("creature") in a hidden zone ("your hand"). Thus, rule 117.8c says that you are not required to cast Disaster Radius, even if directed to do so "if able".
This rule was introduced in the Magic 2014 rules update, specifically to deal with cases like this:
This new rule was added to cover cases where you are instructed to cast a spell with a mandatory additional cost that includes actions involving cards with a stated quality in a hidden zone if able. That's a mouthful. For example, say you're forced to cast Disaster Radius if able. The game doesn't really know if you have a creature card in your hand or not. We don't want you to have to call a judge to verify that you're being honest about the contents of your hand. So, in the spirit of the "fail to find" rule, now you don't have to pay that additional cost and cast the spell.
Technically, before this rule was added, you would have had to reveal a creature card from your hand if you had one; if you did not, you would not have had to reveal your hand to prove this — but you might have been required to ask a judge to inspect your hand and confirm it, if your opponent did not trust your word.
Ps. The "fail to find" rule referenced in the commentary is 701.15b, which says:
701.15b If a player is searching a hidden zone for cards with a stated quality, such as a card with a certain card type or color, that player isn’t required to find some or all of those cards even if they’re present in that zone.
As Jefromi notes in the comment, this rule already covered any situation where one was told to "search" for a card, which is most of them; what it did not cover were a few oddball situations, like this interaction of Wild Evocation with Disaster Radius, that essentially told you to search for a card, but without actually using the word "search". Rule 117.8c patched that hole.
You must reveal a creature card from your hand to cast Disaster Radius in this fashion (as detailed below). If you have no creature cards in your hand, you are unable to pay the cost to cast Disaster Radius, so you are unable to cast Disaster Radius.
If you do have a creature card in your hand, you may chose not to reveal it[CR 117.8c]. If you don't, you are unable to pay the cost to cast Disaster Radius, so you are unable to cast Disaster Radius.
To paraphrase 601.2e,
total cost to cast a spell
= mana cost or alternative cost
"Without paying its mana cost" is an alternative cost[CR 117.9].
"As an additional cost to cast Disaster Radius, reveal a creature card from your hand" is an additional cost[CR 117.8].
So,
total cost to cast Disaster Radius using Wild Evocation
= alternative cost (free)
117.8c. If an effect instructs a player to cast a spell “if able,” and that spell has a mandatory additional cost that includes actions involving cards with a stated quality in a hidden zone, the player isn’t required to cast that spell, even if those cards are present in that zone.
